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W. Adamski, “An abstract approach to weak topologies in spaces of measures,”Bull. Soc. Math. Grèce (N.S.),18, No. 1, 28–68 (1977).
W. Adamski, “On the relations between continuous and nonatomic measures,”Math. Nachr.,99, 55–60 (1980).
W. Adamski, “Note on support-concentrated Borel measures,”J. Austral. Math. Soc., Ser. A,29, 310–315 (1980).
W. Adamski, “Tight set functions and essential measure,”Lect. Notes Math.,945, 1–14 (1982).
W. Adamski, “Extensions of tight set functions with applications in topological measure theory,”Trans. Amer. Math. Soc.,283, No. 1, 353–368 (1984).
W. Adamski, “Factorization of measures and perfection,”Proc. Amer. Math. Soc.,97, No. 1, 30–32 (1986).
W. Adamski, P. Gänssler, and S. Kaiser, “On compactness and convergence in spaces of measures,”Math. Ann.,220, 193–210 (1976).
L. G. Afanas'eva and Yu. G. Petunin, “σ-Algebras generated by comparable normed topologies,” In:Tr. Inst. Mat. Voronezh. Univ. [in Russian], No. 1 (1971), pp. 3–11.
J.-M. Aldaz, “On τ-smooth measure spaces without thick Lindelöf subsets,”Real Anal. Exchange,17, No. 1, 379–385 (1991/92).
A. D. Alexandroff, “Additive set functions in abstract spaces,”Mat. Sb. (N.S.) 8(50), 307–348 (1940); ibid. (N.S.) 9(51), 563–628 (1941); ibid. (N.S.) 13(55), 169–238 (1943).
P. Alexandroff, “Sur la puissance des ensembles mesurables B,”C.R. Acad. Sci. Paris,162, 323–325 (1916).
I. Amemiya, S. Okada, and Y. Okazaki, “Pre-Radon measures on topological spaces,”Kodai Math. J.,1, 101–132 (1978).
B. Anger and C. Portenier, “Radon integrals,”Progress in Mathematics,103, Birkhäuser Boston, Inc., Boston, MA (1992).
B. Anger and C. Portenier, “Radon integrals and Riesz representation,” In:Measure Theory, Oberwolfach (1990) B. Pettineo and P. Vetro, eds.,Rend. Circ. Mat., Palermo (2) Suppl. No. 28 (1992), pp. 269–300.Circolo Matematico di Palermo, Palermo (1992).
A. V. Arkhangelskii and V. I. Ponomarev,Foundations of General Topology in Problems and Exercises [in Russian], Nauka, Moscow (1974).
Th. Armstrong, “Borel measures on compact groups are meager,”Illinois J. Math.,25, No. 4, 667–672 (1981).
N. Aronszajn, “Differentiability of Lipschitzian mappings between Banach spaces,”Studia Math.,57, No. 2, 147–190 (1976).
A. Ascherl and J. Lehn, “Two principles for extending probability measures,”Manusc. Math.,21, 43–50 (1977).
J.-M. Ayerbe-Toledano, “Category measures on Baire spaces,”Publ. Mat.,34, No. 2, 299–305 (1990).
A. G. Babiker, “On almost discrete spaces,”Mathematika,18, 163–167 (1971).
A. G. Babiker, “Some measure theoretic properties of completely regular spaces,”Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.,59, 362–367, 677–681 (1975).
A. G. Babiker, “On uniformly regular topological measure spaces,”Duke Math. J.,43, No. 4, 773–789 (1976).
A. G. Babiker, “Lebesgue measures on topological spaces,”Mathematika,24, 52–59 (1977).
A. G. Babiker, “Uniformly regular sets of measures on completely regular spaces,”Bull. Soc. Math. Grèce (N.S.),21, 122–134 (1980).
A. G. Babiker and S. Graf, “Homomorphism-compact spaces,”Canad. J. Math.,35, No. 3, 558–576 (1983).
A. G. Babiker, G. Heller, and W. Strauss, “On a lifting invariance problem,”Lect. Notes Math.,1089, 79–85 (1984).
A. G. Babiker and J. Knowles, “An example concerning completion regular measures, images of measurable sets and measurable selections,”Mathematika,25, 120–124 (1978).
A. G. Babiker and W. Straus,, “The pseudostrict topology on function spaces,”Rend. Istit. Mat. Univ. Trieste,14, No. 1-2, 99–105 (1982).
G. Bachman, and P. D. Stratigos, “On measure repleteness and support for lattice regular measures,”Internat. J. Math. Sci.,10, No. 4, 707–724 (1987).
G. Bachman and A. Sultan, “Applications of functional analysis to topological measure theory,”Research Notes in Math.,38, 122–164, Pitman, San Francisco (1979).
G. Bachman and A. Sultan, “On regular extensions of measures,”Pacif. J. Math.,86, No. 2, 389–395 (1980).
G. Bachman and A. Sultan, “Extensions of regular lattice measures with topological applications,”J. Math. Anal. Appl.,57, No. 3, 539–559 (1977).
A. Badrikian, “Séminaire sur les fonctions aléatoire linéaires et les mesures cylindriques,”Lect. Notes Math.,139 (1970).
R. Baire,Leçons sur les Fonctions Discontinues, Gauthier Villars, Paris (1898).
A. Balbas de la Corte, “The relation between strongly regular Radon measures and σ-finite measures” [in Spanish],Rev. Real Acad. Cienc. Exact. Fis.-Natur., Madrid,81, No. 1, 223–228 (1987).
T. O. Banakh, and R. Cauty, “Topological classification of spaces on probability measures of co-analytic sets,”Mat. Zametki,55, No. 1, 9–19 (1994); English translation:Math. Notes,55, No. 1-2, 8–13 (1994).
H. Bauer,Mass- und Integrationstheorie, Walter de Gruyter & Co., Berlin (1990).
H. Becker and A. Kechris, “Borel actions of Polish groups,”Bull. Amer. Math. Soc.,28, No. 2, 334–341 (1993).
A. Bellow, “Lifting compact spaces,”Lect. Notes Math.,794, 233–253 (1980).
V. Bentkus, F. Götze, V. Paulauskas, and A. Rachkauskas,The Accuracy of Gaussian Approximations in Banach Spaces, Encyclopedia of Mathematical Sciences, Springer (1994).
S. K. Berberian,Measure Theory and Integration, New York (1965).
I. Berezanski, “Measures on uniform spaces and molecular measures,”Trans. Moscow Math. Soc.,19, 1–40 (1968).
H. Bergstrom,Weak Convergence of Measures, Academic Press, New York-London (1982).
H. Bergstrom, “On weak convergence of sequences of measures,” In:Mathematical Statistics, Banach Center Publ., 6, PWN, Warsaw (1980), pp. 65–72.
D. Bierlein, “Über die Fortsetzung von Wahrscheinlichkeitsfeldern,”Z. Wahr. theor. verw. Geb.,1, 28–46 (1962).
P. Billingsley,Convergence of Probability Measures, Wiley, New York (1968).
P. Billingsley,Weak Convergence of Measures: Applications in Probability, SIAM, Philadelphia, PA (1971).
P. Billingsley and F. Topsøe, “Uniformity in weak convergence,”Z. Wahr. theor. verw. Geb.,7, 1–16 (1967).
G. Birkhoff,Lattice Theory, Providence, Rhode Island (1967).
D. H. Blackwell, “On a class of probability spaces,”Proc. Third Berkeley Symposium on Math. Statistics and Probability (Berkeley, 1954/55), pp. 1–6, Univ. California Press, Berkeley, California (1956).
D. Blackwell and L. E. Dubins, “On existence and nonexistence of proper, regular, conditional distributions,”Ann. Probab.,3, 741–752 (1975).
D. Blackwell and A. Maitra, “Factorization of probability measures and absolutely measurable sets,”Proc. Amer. Math. Soc.,92, No. 2, 251–254 (1984).
D. Blackwell and C. Ryll-Nardzewski, “Non-existence of everywhere proper conditional distributions,”Ann. Math. Statist.,34, 223–225 (1963).
W. W. Bledsoe and A. P. Morse, “Product measures,”Trans. Amer. Math. Soc.,79, 173–215 (1955).
V. I. Bogachev, “Negligible sets in locally convex spaces,”Math. Notes,36, 519–526 (1984).
V. I. Bogachev, “Three problems of Aronszajn from measure theory,”Funct. Anal. Appl.,18, 242–244 (1984).
V. I. Bogachev, “Some results on differentiable measures,”Mat. SSSR Sb.,55, No. 2, 335–349 (1986).
V. I. Bogachev, “Indices of asymmetry of stable measures,”Math. Notes,40, 569–575 (1986).
V. I. Bogachev, “Locally convex spaces with the CLT property and supports of measures,”Moscow Univ. Math. Bull.,41, No. 6, 19–23 (1986).
V. I. Bogachev, “Gaussian measures on linear spaces,”J. Math. Sci.,16, 63–167 (1995); translated from:Itogi Nauki i Tekhn. VINITI,Sovrem. Mat. i Pril., Analiz-8 (1995).
V. I. Bogachev, “Differentiable measures and the Malliavin calculus, Scuola Normale Superiore di Pisa,” Preprint No. 16 (1995), 197 pp.
V. I. Bogachev and Yu. I. Prostov, “A polynomial diffeomorphism of a ball without invariant measures,”Funct. Anal. Appl.,23, No. 4, 75–76 (1989).
V. I. Bogachev and M. Röckner, “Mehler formula and Ornstein-Uhlenbeck processes with general linear drift,”Osaka J. Math.,32, 237–274 (1995).
V. I. Bogachev and O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions,”Russian Math. Surveys,45, No. 3, 1–104 (1990).
N. N. Bogoluboff (Bogolubov) and N. M. Krylov, “La théorie générale de la mesure dans son application à l'étude de systèmes dynamiques de la mécanique non-linéaire,”Ann. Math.,38, 65–113 (1937).
E. Borel,Leçons sur la théorie des fonctions, Gauthier Villars, Paris (1898).
C. Borell, “Convex measures on locally convex spaces,”Ark. Math.,12, 239–252 (1974).
C. Borell, “Gaussian Radon measures on locally convex spaces,”Math. Scand.,38, No. 2, 265–284 (1976).
C. Borell, “A note on Gauss measures which agree on small balls,”Ann. Inst. H. Poincare, Sect. B,13, No. 3, 231–238 (1977).
C. Borell, “A hote on conditional probabilities of a convex measure,”Lect. Notes Phys.,77, 68–72 (1978).
A. A. Borovkov, “Convergence of measures and random processes,”Russian Math. Surveys,31, No. 2, 1–69 (1976).
N. Bourbaki,Topologie Générale, Hermann, Paris.
N. Bourbaki,Intégration, Hermann, Paris.
A. Bouziad and J. Calbrix, “Théorie de la mesure et de l'intégration,”Publ. de l'Univ. de Rouen, 185, Mont-Saint-Aignan (1993).
J. B. Brow and G. V. Cox, “Baire category in spaces of probability measures II,”Fund. Math.,121, No. 2, 143–148 (1984).
V. V. Buldygin,Convergence of Random Elements in Topological Spaces, Naukova Dumka, Kiev (1980).
V. V. Buldygin, “Supports of probability measures in separable Banach spaces,”Theory Probab. Appl.,29, 546–549 (1984).
V. V. Buldygin and A. B. Kharazishvili,Brunn-Minkowski Inequality and Its Applications, Naukova Dumka, Kiev (1985).
V. V. Buldygin and A. B. Kharazishvili, “Anderson's inequality and unimodal measures,”Teor. Veroyatnost. Mat. Statist., No. 35, 13–27 (1986); English translation:Theory Probab. Math. Statist., No. 35, 13–26 (1987).
M. R. Burke and D. Fremlin, “A note on measurability and almost continuity,”Proc. Amer. Math. Soc.,102, No. 3, 611–612 (1988).
J. Calbrix, “Mesures non σ-finies: desintégration et quelques autres proprietés,”Ann. Inst. H. Poincare, Sect. B,17, No. 1, 75–95 (1981).
S. D. Chatterji, “Disintegration of measures and lifting,” In:Vector and Operator Valued Measures and Applications (Proc. Sympos., Snowbird Resort, Alta, Utah, 1972), Academic Press, New York (1973), pp. 69–83.
S. Chevet, “Quelques nouveaux resultats sur les mesures cylindriques,”Lect. Notes Math.,644, 125–158 (1978).
S. Chevet, “Kernel associated with a cylindrical measure”,Lect. Notes Math.,860, 51–80 (1980).
M. M. Choban, “Descriptive set theory and topology”, In:Progress in Science and Technology. Series on Contemporary Problems of Mathematics, Vol. 51, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1989), pp. 173–237.
J. R. Choksi, “Inverse limits of measure spaces”,Proc. London Math. Soc. (3),8, 321–342 (1958).
J. R. Choksi, “On compact contents”,J. London Math. Soc.,33, 387–398 (1958).
J. R. Choksi, “Automorphisms of Baire measures on generalized cubes. II”,Z. Wahr. theor. verw. Geb.,23, 97–102 (1972).
J. R. Choksi, “Measurable transformations on compact groups”,Trans. Amer. Math. Soc.,184, 101–124 (1973).
J. R. Choksi and D. H. Fremlin, “Completion regular measures on product spaces”,Math. Ann.,241, No. 2, 113–128 (1979).
G. Choquet, “Theory of capacities”,Ann. Inst. Fourier (Grenoble),5, 131–295 (1955).
G. Choquet, “Ensembles ϰ-analytiques et ϰ-sousliniens. Cas général et cas métrique”,Ann. Inst. Fourier (Grenoble),9, 75–81 (1959).
G. Choquet, “Forme abstraite du théorème de capacitabilité”,Ann. Inst. Fourier (Grenoble),9, 83–89 (1959).
G. Choquet, “Sur les ensembles uniformément negligéables”,Séminaire Choquet, 9e année, No. 6 (1970).
J. P. R. Christensen,Topology and Borel Structure, Amsterdam (1974).
J. P. R. Christensen, L. Mejlbro, D. Preiss, and J. Tišer,Uniqueness on Systems of Balls and Differentiation Theorems for Radon Measures in Infinite-Dimensional Spaces, Monograph in preparation.
D. L. Cohn, “Liftings and the construction of stochastic processes”,Trans. Amer. Math. Soc.,246, 429–438 (1978).
H. S. Collins, “Strict topologies in measure theory”, In:Proc. Conf. on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979), pp. 1–13,Contemp. Math.,2,Amer. Math. Soc., Providence, R.I. (1980).
W. Comfort and S. Negrepontis,Continuous Pseudometrics, Marcel Dekker, New York (1975).
C. Constantinescu, “Spaces of measures on topological spaces”,Hokkaido Math. J.,10, 89–156 (1981).
C. Constantinescu, “Spaces of measures on completely regular spaces”,Ann. Acad. Sci. Fenn. Ser. A I Math.,10, 125–137 (1985).
C. Constantinescu,Spaces of Measures, de Gruyter, Berlin (1984).
J. Conway, “The strict topology and compactness in the space of measures”,Trans. Amer. Math. Soc.,126, 474–486 (1967).
J. Conway, “A theorem on sequential convergence of measures and some applications”,Pacif. J. Math.,28, 53–60 (1969).
J. Cooper and W. Schachermayer, “Uniform measures and coSaks spaces”,Lect. Notes Math.,843, 217–246 (1981).
G. V. Cox, “On Prohorov spaces”,Fund. Math.,116, No. 1, 67–72 (1983).
H. Cremers and D. Kadelka, “On weak convergence of stochastic processes with Lusin path spaces”,Manuscripta Math.,45, No. 2, 115–125 (1984).
G. Da Prato and J. Zabszyk,Stochastic Differential Equations in Infinite Dimensions, Cambridge Univ. Press (1992).
Yu. L. Daletskii and S. V. Fomin,Measures and Differential Equations in Infinite-Dimensional Spaces, Nauka, Moscow (1983); English translation: Kluwer (1993).
Yu. L. Daletskii and O. G. Smolyanov, “On the weak sequential completeness of the spaces of Radon measures,”Theor. Probab. Appl.,29, No. 1, 141–147 (1984).
R. B. Darst, “On universal measurability and perfect probability,”Ann. Math. Statist. 42, 352–354 (1971).
R. B. Darst, “C ∞-functions need not be bimeasurable,”Proc. Amer. Math. Soc.,27, 128–132 (1971).
R. B. Darst, “Two singular measures can agree on balls,”Mathematika,20, 224–225 (1973).
R. O. Davies, “Measures not approximable or specifiable by means of balls,”Mathematika,18, 157–160 (1971).
R. Davies, “A non-Prokhorov space,”Bull. London Math. Soc.,3, 341–342 (1971); Addendum ibid.4, 310 (1972).
R. O. Davies, “Some counterexamples in measure theory,” In:Proc. Conf. Topology and Measure III. Pt. 1, 2. J. Flachsmeyer, Z. Frolik, Ju. M. Smirnov, F. Topsøe, and F. Terpe, eds., pp. 49–55. Ernst-Moritz-Arndt Universitat, Greifswald (1982).
C. Dellacherie,Capacités et Processus Stochastiques, Springer, Berlin (1972).
C. Dellacherie, “Un cours sur les ensembles analytiques,” In:Analytic Sets, Proc. Symp. London Math. Soc., Academic Press, New York (1980), pp. 184–316.
W. A. Dembski, “Uniform probability,”J. Theoret. Probab.,3, No. 4, 611–626 (1990).
J. Diestel, “Geometry of Banach spaces,”Lect. Notes Math.,485 (1975).
J. Dieudonné, “Un exemple d'un espace normal non susceptible d'une structure uniforme d'espace complet,”C. R. Acad. Sci. Paris,209, 145–147 (1939).
J. Dieudonné, “Sur la convergence des suites des mesures de Radon,”An. Acad. Brasil Sci.,23, 21–38 277–282 (1951).
J. L. Doob,Stochastic Processes, John Wiley & Sons, New York (1953).
J. L. Doob, “Measure theory,”Graduate Texts in Mathematics,143, Springer-Verlag, New York (1994).
L. Drewnowski, “Toplogical rings of sets, continuous set functions. Integration I, II,”Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.,20, 269–286 (1972).
L. Drewnowski, “Equivalence of Brooks-Jewett, Vitali-Hahn-Saks, and Nikodym theorems,”Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.,20, 725–731 (1972).
L. E. Dubins and D. Heath, “With respect to tail sigma fields, standard measures possess measurable disintegrations,”Proc. Amer. Math. Soc.,88, No. 3, 416–418 (1983).
V. M. Dubrovskii, “On some properties of completely additive set functions and passing to the limit under the integral sign,”Izv. Akad. Nauk SSSR,9, No. 4, 311–320 (1945).
V. M. Dubrovskii, “On some properties of completely additive set functions and their applications to a generalization of a theorem of H. Lebesgue,”Mat. Sb.,20, 317–330 (1947).
V. M. Dubrovskii, “On a basis of a family of completely additive set functions and the properties of the uniform additivity and equicontinuity,”Dokl. Akad. Nauk SSSR,58, 737–740 (1947).
R. M. Dudley, “Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces,”Illinois J. Math.,10, 109–126 (1966).
R. Dudley, “Convergence of Baire measures,”Studia Math.,27, 251–268 (1966); Addendum ibid.51, 275 (1974).
R. M. Dudley, “Measures on nonseparable metric spaces,”Illinois J. Math.,11, 449–453 (1967).
R. M. Dudley, “Distances of probability measures and random variables,”Ann. Math. Stat. 39, 1563–1572 (1967).
R. M. Dudley, “On measurability over product spaces,”,Bull. Amer. Math. Soc.,77, 271–274 (1971).
R. M. Dudley, “A counter-example on measurable processes,” In:Proc. of the sixth Berkeley symposium on mathematical statistics and probability, Vol. II, (Berkeley Calif., 1970/71), pp. 57–66 Univ. California Press, Berkeley, Calif., 1972; correction:Ann. Probab.,1, 191–192 (1973).
R. M. Dudley,Real Analysis and Probability, Wadsworth & Brooks, Pacific Grove, CA (1989).
R. M. Dudley and M. Kanter, “Zero-one laws for stable measures,”Proc. Amer. Math. Soc.,45, No. 2, 245–252 (1974); Correction: ibid.88, No. 4, 689–690 (1983).
N. Dunford and J. Schwarz,Linear Operators, I. General Theory, Interscience Publ., New York (1958).
M. Dzamonja and K. Kunen, “Measures on compactHS spaces”Fund. Math.,143, No. 1, 41–54 (1993).
G. A. Edgar, “Disintegration of measures and the vector-valued Radon-Nikodym theorem,”Duke Math. J.,42, No. 3, 447–450 (1975).
G. A. Edgar, “Measurability in a Banach space. I,”Indiana Math. J. 26, 663–677 (1977).
G. A. Edgar, “Measurability in a Banach space. II,”Indiana Math. J.,28, 559–579 (1979).
G. A. Edgar, “On pointwise-compact sets of measurable functions,”Lect. Notes Math.,945, 24–28 (1982).
G. A. Edgar, “Measurable weak sections,”Illinois J. Math.,20, 630–646 (1976).
R. E. Edwards,Functional Analysis. Theory and Applications, Holt, Rinehart and Winston, New York-London (1965).
R. Engelking,General Topology, Warszawa (1977).
V. D. Erohin, “A note towards measure theory,”Usp. Mat. Nauk,16, No. 3, 175–180 (1961).
M. P. Ershov, “Extensions of measures. Stochastic equations,”Lect. Notes Math.,330, 516–526 (1973).
M. P. Ershov, “Extensions of measures and stochastic equations,”Teor. Veroyatn. Ee Primen,19, No. 3, 457–471 (1974).
M. P. Ershov, “The Choquet theorem and stochastic equations,”Anal. Math.,1 No. 4, 259–271 (1975).
M. P. Ershov, “On some principal problems in the theory of stochastic equations,”Institutsbericht, No. 161 (1980), Johannes Kepler Universität, Linz.
M. P. Ershov, “On a generalization of the lonescu Tulcea construction of a measure by transition kernels,”Lect. Notes Math.,945, 29–33 (1982).
M. Jerschow, “Causal selections and solutions of stochastic equations,”Stochastics Stoch. Reports,50, 161–173 (1994).
S. N. Ethier and T. G. Kurtz,Markov Processes. Characterization and Convergence, John Wiley & Sons, Inc., New York (1986).
H. Federer,Geometric Measure Theory, Springer (1969).
V. V. Fedorchuk, “Probability measures in topology,”Usp. Mat. Nauk,46, No. 1, 41–80 (1991); English translation:Russian Math. Surveys,46 (1991).
J. Fernandez-Novoa, “Sigma-finiteness and regularity of generalized Radon measures,”Collect. Math. [Seminario Matematico de Barcellona. Universidad de Barcelona],41, No. 1, 1–11 (1990).
X. Fernique, “Processus linéaires, processus généralisés,”Ann. Inst. Fourier (Grenoble),17, 1–92 (1967).
X. Fernique, “Une démonstartion simple du théorèm de R.M. Dudley et M. Kanter sur les lois zero-un pour les mesures stables,”Lect. Notes Math.,381, 78–79 (1974).
X. Fernique, “Fonctions aléatoires dans les espaces lusiniens,”Expositiones Math.,8, 289–364 (1990).
X. Fernique, “Convergence en loi de fonctions aléatoires continues ou cadlag, proprietés de compacité des lois,”Lect. Notes Math.,1485, 178–195 (1991).
X. Fernique, “Convergence en loi de variables aléatoires et de fonctions aléatoires, propriétés de compacité des lois. II,”Lect. Notes Math.,1557, 216–232 (1993).
S. Fesmire and P. Hlavac, “A short proof of Alexandroff's theorem,”Research Report,72-4 Dept. Math., Carnegie-Mellon University (1972).
J. Flachsmeyer and S. Lotz, “A survey on hyperdiffuse measures,” In:Proc. Conf. Topology and Measure, I (Zinnowitz, 1974), Pt.1, Ernst-Moritz-Arndt Univ., Greifswald (1978), pp. 87–128.
J. Flachsmeyer and F. Terpe, “Some applications of extension theory for topological spaces and measure theory,”Russian Math. Surveys 32, No. 5, 133–171 (1977).
D. H. Fremlin,Topological Riesz Spaces and Measure Theory, Cambridge Univ. Press, London (1974).
D. H. Fremlin, “Products of Radon measures: a counter-example,”Canad. Math. Bull.,19, No. 3, 285–289 (1976).
D. H. Fremlin,Counter-Example to a “Theorem” of A.G.A.G. Babiker, Preprint (1976).
D. H. Fremlin, “Uncountable powers of ® can be almost Lindelöf,”Manuscripta Math.,22, 77–85 (1977).
D. H. Fremlin, “Borel sets in non-separable Banach spaces,”Hokkaido Math. J.,9, 179–183 (1980).
D. H. Fremlin, “Measurable functions and almost continuous functions,”Manuscripta Math.,33, No. 3-4, 387–405 (1981).
D. H. Fremlin, “On the additivity and confinality of Radon measures,“Mathematika,31, No. 2, 323–335 (1984).
D. H. Fremlin,Consequences of Martin's Axiom, Cambridge Univ. Press (1985).
D. Fremlin, D. Garling, and R. Haydon, “Bounded measures on topological spaces,”Proc. London Math. Soc.,25, 115–136 (1972).
D. Fremlin and S. Grekas, “Products of completion regular measures,”Fund. Math.,147, No. 1, 27–37 (1995).
Z. Frolik, “A survey of separable descriptive theory of sets and spaces,”Czech. Math. J.,20 (95), 406–467 (1970).
Z. Frolik, “Measure-fine uniform spaces. II,”Lect. Notes Math.,945, 34–41 (1982).
S. L. Gale, “Measure-compact spaces,”Topol. Appl.,45, No. 2, 103–118 (1992).
P. Ganssler, “A convergence theorem for measures in regular topological spaces,”Math. Scand.,29, 237–244 (1971).
P. Ganssler, “Compactness and sequential compactness in spaces of measures,”Z. Wahr. theor. verw. Geb.,17, 124–146 (1971).
P. Ganssler, “Empirical processes,”Institute of Mathematical Statistics Lecture Notes, Monograph Series, 3,Institute of Mathematical Statistics, Hayward, Calif. (1983).
R. J. Gardner, “The regularity of Boreal measures and Borel measure-compactness,”Proc. London Math. Soc.,30, 95–113 (1975).
R. J. Gardner, “The regularity of Boreal measures,”Lect. Notes Math.,945, 42–100 (1982).
R. J. Gardner and W. F. Pfeffer, “Borel measures,” in:Handbook of Set-Theoretic Topology, North-Holland, Amsterdam-New York (1984), pp. 961–1043.
D. Garling “A ‘short’ proof of the Riesz representation theorem,”Proc. Camb. Philos. Soc.,73, 459–460 (1973).
P. Gerard, “Suite de Cauchy et compacité dans les espaces de mesures,”Bull. Soc. Roy. Sci. Liège,42, 41–49 (1973).
P. Gerard, “Un critere de compacité dans l'espaceM t + (E),”Bull. Soc. Roy. Sci. Liège,42, 179–182 (1973).
N. Ghoussoub, G. Godefroy, B. Maurey, and W. Schachermayer, “Some topological and geometrical structures in Banach spaces,”Mem. Amer. Math. Soc.,70, No. 378 (1987).
I. I. Gikhman and A. V. Skorohod,The Theory of Stochastic Processes, Vol. 1, Springer-Verlag, Berlin (1979).
I. Glicksberg, “The representation of functionals by integrals,”Duke Math. J.,19, 253–261 (1952).
B. V. Gnedenko and A. N. Kolmogorov,Limit Distributions for Sums of Independent Random Variables [in Russian], GITTL, Moscow (1949); English translation: Addisons-Wesley, Cambridge, MA (1954).
G. Gould and M. Mahowald, “Measures on completely regular spaces,”J. London Math. Soc.,37, 103–111 (1962).
S. Graf and G. Magerl, “Disintegration of a measure with respect to a correspondence,”Lect. Notes Math.,945, 167–169 (1982).
S. Graf and R. D. Mauldin, “A classification of disintegrations of measures,” In: Measure and mesurable dynamics (Rochester, NY, 1987), pp. 147–158.Contemp. Math.,94,Amer. Math. Soc., Providence, RI (1989).
E. E. Granirer, “On Baire measures onD-topological spaces,”Fund. Math.,60, 1–22 (1967).
P. Grassi, “On subspaces of replete and measure replete spaces,”Canad. Math. Bull.,27, No. 1, 58–64 (1984).
F. P. Greenleaf,Invariant Means on Topological Groups and Their Applications, Van Nostrand, New York (1969).
S. Grekas, “On products of completion regular measures,”J. Math. Anal. Appl.,171, No. 1, 101–110 (1992).
S. Grekas, “Isomorphic measures on compact groups,”Math. Proc. Cambridge Philos. Soc.,112, No. 2, 349–360 (1992); Corrigendum: ibid.115, No. 2, 377 (1994).
S. Grekas, “Structural properties of compact groups with measure-theoretic applications,”Israel J. Math.,87, Nos. 1–3, 89–95 (1994).
S. Grekas and C. Gryllakis, “Completion regular measures on product spaces with application to the existence of Baire strong liftings,”Illinois J. Math.,35, No. 2, 260–268 (1991).
S. Grekas and C. Gryllakis, “Measures on product spaces and the existence of strong Baire lifting,”Monatsh. Math.,114, No. 1, 63–76 (1992).
W. Grömig, “On a weakly closed subset of the space of τ-smooth measures,”Proc. Amer. Math. Soc.,43, 397–401 (1974).
A. Grothendieck, “Sur les applications linéaires faiblement compactes d'espaces du typeC(K),”Canad. J. Math.,5, 129–173 (1953).
C. Gryllakis, “Products of completion regular measures,”Proc. Amer. Math. Soc.,103, No. 2, 563–568 (1988).
C. Gryllakis and G. Koumoullis, “Completion regularity and τ-additivity of measures on product spaces,”Compositio Math.,73, 329–344 (1990).
W. Hackenbroch, “Conditionally multiplicative simultaneous extension of measures,” In:Measure theory, Oberwolfach, 1990, B. Pettineo and P. Vetro, eds.;Rend. Circ. Mat. Palermo (2) Suppl. No. 28 (1992), pp. 49–58.
J. Haezendonck “Abstract Lebesgue-Rokhlin spaces,”Bull. Soc. Math. Belgique,25, 243–258 (1973).
H. Hahn and A. Rosenthal,Set Functions, Univ. New Mexico Press (1948).
P. Halmos,Measure Theory, Van Nostrand, New York (1950); (Second ed.: Springer-Verlag (1974)).
P. R. Halmos and J. von Neumann, “Operator methods in classical mechanics. II,”Ann. Math.,43, No. 2, 332–350 (1942).
F. Hausdorff, “Die Mächtigkeit der Borelschen Mengen,”Math. Ann.,77, No. 3, 430–437 (1916).
R. Haydon, “On compactness in spaces of measures and measure compact spaces,”Proc. London Math. Soc.,29, 1–16 (1974).
R. Haydon, “On dualL 1-spaces and injective bidual Banach spaces,”Israel J. Math.,31, 142–152 (1978).
W. Hazod, “Stable probability measures on groups and on vector spaces,”Lect. Notes Math.,1210, 304–352 (1986).
D. J. Hebert and H. E. Lacey, “On supports of regular Borel measures,”Pacif. J. Math.,27, 101–118 (1968).
G. Heller, “On a local version of pseudocompactness,” In:General Topology and Its Relations to Modern Analysis and Algebra V (Prague, 1981),Sigma Ser. Pure Math., Vol. 3, Heldermann, Berlin (1983), pp. 265–271.
P.-L. Hennequin and A. Tortrat,Théorie des Probabilités et Quelques Applications, Masson et Gie (1965).
J. P. Henry, “Prolongements de measures de Radon,”Ann. Inst. Fourier (Grenoble),19, No. 1, 237–247 (1969).
E. Hewitt, “Linear functionals on spaces of continuous functions,”Fund. Math.,37, 161–189 (1950).
H. Heyer,Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin (1977).
J. Hoffmann-Jorgensen, “The theory of analytic spaces,”Aarhus Various Publ. Series, No. 10 (1970).
J. Hoffmann-Jorgensen, “Existence of conditional probabilities,”Math. Scand.,28, 257–264 (1971).
J. Hoffmann-Jorgensen, “A generalization of the strict topology,”Math. Scand.,30, 313–323 (1972).
J. Hoffmann-Jorgensen, “Weak compactness and tightness of subsets ofM(X),”Math. Scand.,31, 127–150 (1972).
J. Hoffmann-Jorgensen, “Probability in Banach spaces,”Lect. Note Math.,598, 1–186 (1976).
J. Hoffmann-Jorgensen, “Integrability of seminorms, the 0–1 law and the affine kernel for product measures,”Studia Math.,61, 137–159 (1977).
J. Hoffmann-Jorgensen, “Stochastic processes on Polish spaces, Various Publications Series,”39, Aarhus Universitet, Matematisk Institut, Aarhus (1991).
B. R. Hunt T. Sauer, and J. A. Yorke, “Prevalence: a translation-invariant “almost-everywhere’ on infinite-dimensional spaces,”Bull. Amer. Math. Soc.,27, 217–238 (1992); Addendum: ibid.28, 306–307 (1993).
A. Ionescu Tulcea and C. Ionescu Tulcea,Topics in the Theory of Lifting, Springer, Berlin (1969).
B. G. Ivanoff, “The function spaceD([0,∞) q,E),”Canad. J. Statist.,8, No. 2, 179–191 (1980).
K. Jacobs,Measure and Integral, Academic Press, New York (1978).
A. Jakubowski, “On the Skorohod topology,”Ann. Inst. H. Poincare Probab. Statist.,22, No. 3, 263–285 (1986).
A. Janssen, “A survey about zero-one laws for probability measures on linear spaces and locally compact groups,”Lect. Notes Math.,1064, 551–563 (1984).
J. Jayne, “Structure of analytic Hausdorff spaces,”Mathematika,23, 208–211 (1976).
J. Jayne, “Generation of σ-algebras, Baire sets, and descriptive Borel sets,”Mathematika,24, 241–256 (1977).
T. Jech,Set Theory, Academic Press, New York (1978).
B. Jefferies and W. J. Ricker, “Integration with respect to vector valued Radon polymeasures,”J. Austral. Math. Soc. Ser. A,56, No. 1, 17–40 (1994).
P. Jimenez-Guerra, “On the convergence of means,”Rev. Real Acad. Cienc. Exact. Fis. Natur., Madrid72, No. 4, 610–612 (1978).
P. Jimenez-Guerra and B. Rodriguez-Salinas, “Strictly localizable measures,”Nagoya Math. J.,85, 81–86 (1982).
M. Jirina, “Conditional probabilities on algebras with countable base,”Czech. Math. J.,4 (79) 372–380 (1954).
M. Jirina, “On regular conditional probabilities,”Czech. Math. J.,9, 445–451 (1959).
R. A. Johnson, “On product measures and Fubini's theorem in locally compact spaces,”Trans. Amer. Math. Soc.,123, 112–129 (1966).
R. A. Johnson, “Measurability of cross section measures of a product Borel set,”J. Austral. Math. Soc. Ser. A.,28, 346–352 (1979).
R. A. Johnson, “Nearly Borel sets and product measures,”Pacif. J. Math.,87, 97–109 (1980).
R. A. Johnson, “Extending the product of two regular Boreal measures,”Illinois J. Math.,24, 639–644 (1980).
R. A. Johnson, “Disintegrating measures on compact group extensions,”Z. Wahrsch. Verw. Geb.,53, No. 3, 271–281 (1980).
R. A. Johnson, “Another Borel measure-compact space which is not weakly Borel-measure complete,”J. London Math. Soc.,21, 263–264 (1980).
R. A. Johnson, “Products of two Borel measures,”Trans. Amer. Math. Soc.,269, No. 2, 611–625 (1982).
R. A. Johnson and W. Wilczynski, “Finite products of Borel measures,” In:Measure Theory (Oberwolfach, 1990), B. Pettineo and P. Vetro, eds.;Rend, Circ. Mat. Palermo (2) Suppl. No. 28 (1992), pp. 141–148;Circolo Matematico di Palermo, Palermo (1992), pp. 1–448.
I. Juhasz, “Cardinal functions in topology,”Math. Centre, No. 34,Mathematisch Centrum, Amsterdam (1971).
I. Juhasz, K. Kunen and M. E. Rudin, “Two more hereditarily separable non-Lindelöf spaces,”Canad. J. Math.,5, 998–1005 (1976).
S. Kakutani, “Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions),”Ann. Math. Ser. 2,42, 994–1024 (1941).
V. G. Kanovei,The Axion of Choice and the Axiom of Determinateness [in Russian], Nauka, Moscow (1984).
M. Kanter, “Linear sample spaces and stable processes,”J. FUnct. Anal.,9, 441–459 (1972).
M. Kanter, “Random linear functionals and why we study them,”Lect. Notes Math.,645, 114–123 (1978).
M. Katetov, “Measures in fully normal spaces,”Fund. Math.,38, 73–84 (1951).
A. B. Katok and A. M. Stepin, “Metric properties of measure-preserving homeomorphisms,”Russian Math. Surveys,25, 191–220 (1970).
M. P. Kats, “Continuity of universally measurable linear mappings,”Sib. Mat. Zh.,23, No. 3, 83–90 (1982); correction; ibid.24, No. 3, 217 (1983).
J. Kawabe, “Convergence of compound probability measures on topological spaces,”Colloq. Math.,67, No. 2, 161–176 (1994).
H. G. Kellerer, “Baire sets in product spaces,”Lect. Notes Math.,794, 38–44 (1980).
H. G. Kellerer, “Duality theorems for marginal problems,”Z. Wahrsch. Verw. Geb.,67, No. 4, 399–432 (1984).
J. H. B. Kemperman and D. Maharam, “ℝc is not almost Lindelöf,”Proc. Amer. Math. Soc.,24, 772–773 (1970).
A. B. Kharazishvili,Topological Aspects of Measure Theory, Naukova Dumka, Kiev (1984).
A. B. Kharazishvili,Applications of Set Theory, Tbilis. Gos. Univ., Tbilisi (1989).
A. B. Kharazishvili, “Borel measures in metric spaces,”Soobshch. Akad. Nauk. Gruzin. SSR,135, No. 1, 37–40 (1989).
A. R. Kharazishvili, “Some problems in measure theory,”Colloq. Math.,62, 197–220 (1991).
A. Yu. Khrennikov, “Measures with Hilbertian supports on topological linear spaces,”Vestn. Mosk. Univ., No. 4, 47–49 (1981); English translation:Moscow Univ. Math. Bull.,36 (1981).
S. S. Khurana, “Convergent sequences of regular measures,”Bull. Acad. Sci. Polon., Sér. Math. 24, No. 1, 37–41 (1976).
R. B. Kirk, “Measures in topological spaces and B-compactness,”Indag. Math.,31 (Nedel. Akad. Wetensch. Proc. Ser. A,72), 172–183 (1969).
R. B. Kirk, “Topologies on spaces of Baire measures,”Bull. Amer. Math. Soc.,79, 542–545 (1973).
R. B. Kirk, “Complete topologies on spaces of Baire measures”,Trans. Amer. Math. Soc.,184, 1–21 (1973).
R. B. Kirk, “Convergence of Baire measures,”Pacif. J. Math.,49, 135–148 (1973).
R. B. Kirk and J. Crenshaw, “A generalized topological measure theory,”Trans. Amer. Math. Soc.,207, 189–217 (1975).
J. Kisynski, “On the generation of tight measures,”Studia Math.,30, 141–151 (1968).
V. M. Klimkin, “Some properties of regular set functions”,Mat. Sb.,183, No. 6, 155–176 (1992); English translation:Russian Acad. Sci. Sb. Math.,76, No. 1, 247–263 (1993).
J. Knowles, “On the existence of non-atomic measures,”Mathematika,14, 62–67 (1967).
J. Knowles, “Measures on topological spaces,”Proc. London Math. Soc.,17, 139–156 (1967).
A. N. Kolmogorov,Grundbegriffe der Wahrscheinlichkeitsrechnung, Berlin (1933); English translation:Foundations of the Theory of Probability, Chelsea Publ. Co., New York (1950).
A. N. Kolmogorov, “La transformation de Laplace dans les espaces linéaires,”C.R. Acad. Sci.,200, 1717–1718 (1935).
A. N. Kolmogorov, “Remarks on the papers of R. A. Minlos and V. V. Sazonov,”Theor. Probab. Appl.,4, 221–223 (1959).
A. N. Kolmogorov and S. V. Fomin,Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1976).
A. N. Kolmogorov and Yu. V. Prohorov, “Zufällige Funktionen und Grenzverteilugssätze,”Bericht über die Tagung Wahrscheinlichkeitsrechnung und mathematische Statistik, Berlin, 113–126 (1956).
H. Konig, “On inner/outer regular extensions of contents,” In:Measure Theory, Oberwolfach, 1990, B. Pettineo and P. Vetro, eds.Rend. Circ. Mat. Palermo (2) Suppl. No. 28 (1992), pp. 59–85.Circolo Matematico di Palermo, Palermo (1992), pp. 1–447.
G. Koumoullis, “On perfect measures,”Trans. Amer. Math. Soc.,264, No. 2, 521–537 (1981).
G. Koumoullis, “Some topological properties of spaces of measures,”Pacif. J. Math.,96, No. 2, 419–433 (1981).
G. Koumoullis, “Perfect,u-additive measures and strict topologies,”Illinois J. Math.,26, No. 3, 466–478 (1982).
G. Koumoullis, “On the almost Lindelöf property in products of separable metric spaces,”Compositio Math.,48, No. 1, 89–100 (1983).
G. Koumoullis, “Cantor sets in Prohorov spaces,”Fund. Math.,124, 155–161 (1984).
G. Koumoullis, “Topological spaces containing compact perfect sets and Prohorov spaces,”Topol. Appl.,21, 59–71 (1985).
G. Koumoullis and K. Prikry, “The Ramsey property and measurable selections,”J. London Math. Soc. (2),28, 203–210 (1983).
G. Koumoullis and K. Prikry, “Perfect measurable spaces,”Ann. Pure Appl. Logic,30, No. 3, 219–248 (1986).
G. Koumoullis and K. Sapounakis, “Two countability properties of sets of measures,”Michigan Math. J.,31, 31–47 (1984).
V. M. Kruglov,Additional Chapters of Probability Theory [in Russian], Visshaya Shkola, Moscow (1984).
J. Kuelbs, “Some results for probability measures on linear topological vector spaces with an application to Strassen's LogLog Law,”J. Funct. Anal.,14, No. 1, 28–43 (1973).
V. G. Kulakova, “Regularity of conditional probabilities,”Vestn. Leningrad. Univ., No. 1(1), 16–20 (1976).
K. Kunen, “CompactL-spaces,”Topol. Appl.,12, 283–287 (1981).
K. Kunen and J. van Mill, “Measures on corson compact spaces,”Fund. Math.,147, No. 1, 61–72 (1995).
K. Kuratowski,Topology, Vol. 1, 2, Academic Press, New York-London (1966).
K. Kuratowski and A. Mostowski,Set Theory, North-Holland Publ., Amsterdam (1967).
L. Le Cam, “Un instrument d'étude des fonctions aléatoires: la fonctionnelle caractéristique,”C.R. Acad. Sci. Paris,224, 710 (1947).
L. Le Cam, “Convergence in distribution of stochastic processes,”Univ. Calif. Publ. Statist.,2, 207–236 (1957).
M. Ledoux and M. Talagrand,Probability in Banach Spaces. Isoperimetry and Processes, Springer-Verlag, Berlin-New York (1991).
J. Lembcke, “Konservative Abbildungen und Fortsetzung regulärer Masse,”Z. Wahr. Verw. Geb.,15, 57–96 (1970).
J. Lembcke, “Reguläre Masse mit einer gegebenen Familie von Bildmassen,”Bayer. Akad. Wiss. Math., Naturw. Kl. Sitzungsber. 1976, 61–115 (1977).
J. Lembcke, “On a measure extension theorem of Bierlein,”Lect. Notes Math.,794, 45–48 (1980).
J. Lembcke, “A set function without σ-additive extension having finitely additive extensions arbitrarily close to σ-additivity,”Czech. Math. J.,30, 376–381 (1980).
J. Lembcke, “On simultaneous preimage measures on Hausdorff spaces,”Lect. Notes Math.,945, 110–115 (1982).
V. L. Levin,Convex Analysis in Spaces of Measurable Functions and Its Application in Mathematics and Economics [in Russian], Nauka, Moscow (1985).
M. A. Lifshits,Gaussian Random Functions, Kluwer Acad. Publ. (1995).
W. Linde,Probability in Banach Spaces — Stable and Infinitely Divisible Distributions, Wiley (1986).
E. R. Lorch, “Compactification, Baire functions, and Daniell integration,”Acta Sci. Math. (Szeged),24, 204–218 (1963).
V. Losert, “A measure space without the strong lifting property,”Math. Ann.,329, No. 2, 119–128 (1979).
V. Losert, “A counterexample on measurable selections and strong lifting,”Lect. Notes Math.,794, 153–159 (1980).
V. Losert, “Strong liftings for certain classes of compact spaces,”Lect. Notes Math.,945, 170–179 (1982).
J. Loś and E. Marchewski, “Extensions of measure,”Fund. Math. 36, 267–276 (1949).
S. Lotz, “A survey on hyperdiffuse measures. IV,” In:Proc. of the Conf. Topology and Measure III. Pt. 1, 2, J. Flachsmeyer, Z. Frolik, Yu. M. Smirnov, F. Topsoe, and F. Terpe, eds., Vitte (1980), pp. 127–163; Hiddensee (1980), Univ. Greifswald (1982).
N. Lusin, “Sur la classification de M. Baire,”C.R. Sci. Acad. Paris,164, 91–94 (1917).
N. Lusin,Leçons sur les Ensembles Analytiques et Leurs Applications, Gauthiers-Villars, Paris (1930).
A. M. Lyapunov,Problems of Set Theory and the Theory of Functions [in Russian], Nauka, Moscow (1979).
Z. Ma, “Some results on regular conditional probabilities,”Acta Math. Sinica, New Series,1, No. 4, 302–307 (1985).
Z. M. Ma and M. Röckner,An Introduction to the Theory of (Non-Symmetric) Direchlet Forms, Springer, Berlin (1992).
N. D. Macheras and W. Strauss, “On the permanence of almost strong liftings,”J. Math. Anal. Appl.,174, No. 2, 566–572 (1993).
N. D. Macheras and W. Strauss, “On various strong lifting properties for topological measure spaces,” In:Measure Theory, Oberwolfach, 1990, B. Pettineo and P. Vetro, eds.Rend. Circ. Mat. Palermo (2) Suppl. No. 28 (1992), pp. 149–162.Circolo Matematico di Palermo, Palermo (1992), pp. 1–447.
N. D. Macheras and W. Strauss, “On completion regularity and Baire almost strong liftings,”Atti Sem. Mat. Fis. Univ. Modena,42, No. 1, 199–209 (1994).
N. D. Macheras and W. Strauss, “On strong liftings for projective limits,”Fund. Math.,144, No. 3, 209–229 (1994).
D. Maharam, “On homogeneous measure algebras,”Proc. Natl. Acad. Sci. USA,28, 108–111 (1942).
D. Maharam, “On a theorem of von Neumann,”Proc. Amer. Math. Soc.,9, 987–994 (1958).
D. Maharam, “From finite to countable additivity,”Portugal. Math.,44, No. 3, 265–282 (1987).
A. Maitra, “Co-analytic sets are not Blackwell spaces,”Fund. Math.,67, No. 2, 251–254 (1970).
A. Maitra, “A note on bimeasurable functions,”Bull. Acad. Polon. Sci., Sér. Math.,23, No. 2, 131–134 (1975).
A. Maitra, “Integral representations of invariant measures,”Trans. Amer. Math. Soc.,229, 209–225 (1977).
A. Maitra and S. Ramakrishnan, “Factorization of measures and normal conditional distributions,”Proc. Amer. Math. Soc.,103, No. 4, 1259–1267 (1988).
E. Marczewski, “On compact measures,”Fund. Math.,40, 113–124 (1953).
E. Marczewski and R. Sikorski, “Measures in non-separable metric spaces,”Colloq. Math.,1, 133–139 (1948).
J. L. de Maria and B. Rodriguez-Salinas, “The space (l ∞/c O, weak) is not a Radon space,”Proc. Amer. Math. Soc.,112, No. 4, 1095–1100 (1991).
J. L. de Maria and B. Rodriguez-Salinas, “On measurable sets of a τ-additive measure,” In:Papers in Honor of Pablo Bobillo Guerrero, Univ. Granada, Granada (1992), pp. 241–259.
J. L. de Maria and B. Rodriguez-Salinas, “Banach spaces which are Radon spaces with the weak topology,”Bull. London Math. Soc.,25, No. 6, 577–581 (1993).
J. Mařík, “The Baire and Borel measures,”Czech. Math. J.,7, (82), 248–253 (1957).
J. Mařík, “Les fonctionnelles sur l'ensemble des fonctions continues bornées, définies dans un espace topologique,”Studia Math.,16, 86–94 (1957).
A. A. Markov, “On mean values and exterior densities,”Mat. Sb.,4 (46), 165–191 (1938).
R. D. Mauldin, “Baire functions, Borel sets, and ordinary function systems,”Adv. Math.,12, 418–450 (1974).
R. D. Mauldin, “Borel parametrizations,”Trans. Amer. Math. Soc.,250, 223–234 (1979).
R. D. Mauldin and A. H. Stone, “Realization of maps,”Lect. Notes Math.,945, 145–149 (1982).
L. Mejlbro, D. Preiss, and J. Tiser, “Positivity principles in geometrical measure theory,” In:Measure Theory, Oberwolfach, 1990, B. Pettineo and P. Vetro, eds.Rend. Circ. Mat. Palermo (2) Suppl. No. 28 (1992), pp. 163–167.Circolo Matematico di Palermo, Palermo (1992), pp. 1–447.
P.-A. Meyer,Probability and Potentials, Blaisdell Publ. Co. (1965).
R. A. Minlos, “Generalized random processes and their extension to a measure,”Tr. Mosk. Mat. Obsch.,8, 497–518 (1959); English translation:Math. Stat. Probab.,3, 291–314 (1959).
I. Mitoma, “Tightness of probabilities onC([0, 1];S′) andD([0, 1];S′),”Ann. Probab.,11, No. 4, 989–999 (1983).
J. Mohapl, “On weakly convergent nets in spaces of nonnegative measures,”Crech. Math. J.,40, (115), No. 3, 408–421 (1990).
J. Mohapl, “Non-Borel measures on nonseparable metric spaces,”Math. Slovaca,40, No. 4, 413–422 (1990).
J. Mohapl, “The Radon measures as functionals on Lipschitz functions,”Czech. Math. J.,41, No. 3, 446–453 (1991).
W. Moran, “The additivity of measures on completely regular spaces,”J. London Math. Soc.,43, 633–639 (1968).
W. Moran, “Measures and mappings on topological spaces”,Proc. London Math. Soc.,19, 493–508 (1969).
W. Moran, “Measures on metacompact spaces,”Proc. London Math. Soc.,20, 507–524 (1970).
S. E. Mosiman and R. F. Wheeler, “The strict topology in a completely regular setting: relations to topological measure theory,”Canad. J. Math.,24, 873–890 (1972).
D. Mouchtari, “La topologie du type de Sazonov pour les Banach et les supports hilbertiens,”Ann. Univ. Clermont.,61, 77–87 (1976).
P. Muldowney, “A general theory of integration in function spaces, including Wiener and Feynman integration,”Pitman Research Notes in Math. Series,153. Longman Scientific, Wiley, New York (1987).
D. Kh. Mushtari,Probability and Topology in Banach Spaces [in Russian], Izd. Kazan Univ., Kazan (1988).
K. Musial, “Existence of proper conditional probabilities,”Z. Wahr. theor. verw. Geb.,22, 8–12 (1972).
K. Musial, “Inheritedness of compactness and perfectness of measures by thick subsets,”Lect. Notes Math.,541, 31–42 (1976).
K. Musial, “Projective limits of perfect measure spaces,”Fund. Math.,110, 163–189 (1980).
S. Nakanishi, “Weak convergence of measures on the union of metric spaces. I,”Math. Japon.,31, No. 3, 429–447 (1986).
J. von Neumann, “Algebraische Repräsentaten der Funktionen ‘bis auf eine Menge vom Masse Null’,”J. Reine Ang. Math.,165, 109–115 (1931).
J. von Neumann, “Einige Sätze über messbare Abbildungen,”Ann. Math.,33, 574–586 (1932).
J. Neveu,Bases Mathématiques du Calcul des Probabilités, Masson et Cie, Paris (1964).
Nghiem Djang Ngoc, “A remark on disintegrations with almost all components non σ-additive,”Canad. J. Math.,31, No. 4, 786–788 (1979).
S. Okada, “Supports of Borel measures,”J. Austral. Math. Soc.,27, 221–231 (1979).
S. Okada and Y. Okazaki, “On measure-compactness and Porel measure-compactness,”Osaka Math. J.,15, 183–191 (1978).
H. Ohta and K. Tamano, “Topological spaces whose Baire measure admits a regular Borel extension,”Trans. Amer. Math. Soc.,317, No. 1, 393–415 (1990).
U. Oppel, “Zur charakterisierung Suslinscher und Lusinscher Räume,”Z. Wahr. theor. verw. Geb.,34, 183–192 (1976).
U. Oppel, “Zur schwachen Topologie auf dem Vektorraum der Borel-Masse Polnischer und Lusinscher Räume,”Math. Z.,147, 97–99 (1976).
J. C. Oxtoby, “Homeomorphic measures in metric spaces,”Proc. Amer. Math. Soc.,24, 419–423 (1970).
J. C. Oxtoby,Measure and Category, Springer, New York (1971).
J. C. Oxtoby and S. Ulam, “Measure-preserving homeomorphisms and metrical transitivity,”Ann. Math. Ser. 2,42, 874–920 (1941).
J. K. Pachl, “Disintegration and compact measures,”Math. Scand.,43, No. 1, 157–168 (1978/79).
J. K. Pachl, “Two classes of measures,”Colloq. Math.,42, 331–340 (1979).
J. K. Pachl, “Measures as functionals on uniformly continuous functions,”Pacif. J. Math.,82, 515–521 (1979).
J. K. Pachl,Mathematical Reviews, 81h 60005b (1981).
R. Panzone and C. Segovia, “Measurable transformations on compact spaces and o.n. systems on compact groups,”Rev. Un. Mat. Urgentina,22, 83–102 (1964).
E. Pap, “Regular Borelt-decomposable measures,”Zb. Rad. Prirod. Mat. Fak. Ser. Mat.,20, No. 2, 113–120 (1990).
K. R. Parthasarathy,Probability Measures on Metric Spaces, Academic Press, New York (1967).
K. R. Parthasarathy,Introduction to Probability and Measure (1980).
J. Pellaumail, “Application de l'existence d'un relèvement à un théorème sur la désintégration de mesures,”Ann. Inst. H. Poincare, Sect. B (N.S.),8, 211–215 (1972).
M. Penconek and P. Zakrzewski, “The existence of nonmeasurable sets for invariant measures,”Proc. Amer. Math. Soc.,121, No. 2, 579–584 (1994).
M. D. Perlman, “Characterizing measurability, distribution and weak convergence of random variables in a Banach space by total subsets of linear functionals,”J. Multivar. Anal.,2, No. 3, 174–188 (1972).
J. Pfanzagl, “Convergent sequences of regular measures,”Manuscripta Math.,4, 91–98 (1971).
J. Pfanzagl and W. Pierlo, “Compact systems of sets,”Lect. Notes Math.,16 (1966).
W. F. Pfeffer,Integrals and Measures, Marcel Dekker, New York (1977).
R. R. Phelps,Lectures on Choquet's Theorem, Van Nostrand Inc., Princeton (1966).
R. R. Phelps, “Gaussian null sets and differentiability of Lipschitz map on Banach spaces,”Pacif. J. Math.,77, No. 2, 523–531 (1978).
D. Plachky, “On semiregular conditional distributions,”J. Theoret. Probab.,5, No. 3, 577–584 (1992).
G. Plebanek, “On strictly positive measures on topological spaces,”Atti Sem. Mat. Fis. Univ. Modena,39, No. 1, 181–191 (1991).
G. Plebanek, “Families of sets of positive measure,”Trans. Amer. Math. Soc.,332, No. 1, 181–191 (1992).
R. Pol, “Note on the spacesP(S) of regular probability measures whose topology is determined by countable subsets,”Pacif. J. Math.,100, No. 1, 185–201 (1982).
D. Pollard, “Induced weak convergence and random measures,”Z. Wahrsch. Verw. Geb.,37, No. 4, 321–328 (1976/77).
D. Pollard, “Compact sets of tight measures,”Studia Math.,56, 63–67 (1976).
D. Pollard, “Weak convergence on nonseparable metric spaces,”J. Austral. Math. Soc. Ser. A,28, No. 2, 197–204 (1979).
D. Pollard,Convergence of Stochastic Processes, Springer, Berlin-New York (1984).
D. Pollard and F. Topsøe, “A unified approach to Riesz-type representation theorems,”Studia Math.,54, 173–190 (1975).
V. S. Prasad, “A survey of homeomorphic measures,”Lect. Notes Math.,945, 150–154 (1982).
D. Preiss, “Metric spaces in which Prohorov's theorem is not valid,”Z. Wahrsch. verw. Geb.,27, 109–116 (1973).
D. Preiss, “Differentiation of measures in infinitely-dimensional spaces,” In:Proc. of the Conf. Topology and Measure III. Pt. 1, 2. J. Flachsmeyer, Z. Frolik, Ju. M. Smirnov, F. Topsoe, and F. Terpe, eds., Ernst-Moritz-Arndt Universitat, Greifswald (1982), pp. 201–207.
D. Preiss and J. Tiser, “Differentiation of measures on Hilbert spaces,”Lect. Notes Math.,945, 194–207 (1982).
D. Preiss and J. Tiser, “Measures in Banach spaces are determined by their values on balls,”Mathematika,38, 391–397 (1991).
S. M. Prigarin, “Weak convergence of probability measures in spaces of continuously differentiable functions,”Sib. Mat. Zh.,34, No. 1, 140–144 (1993); English translation:Sib. Math. J.,34, No. 1, 123–127 (1993).
Yu. V. Prohorov, “Convergence of random processes and limit theorems in probability theory,”Theor. Probab. Appl.,1, 157–214 (1956).
Yu. V. Prohorov, “The method of characteristic functionals,” In:Proc. 4th Berkeley Symp. on Math. Statistics and Probability, Vol. 2, Berkeley, University of California Press (1960), pp. 403–419.
R. Purves, “Bimeasurable functions,”Fund. Math.,58, 149–157 (1966).
D. A. Raikov, “On two classes of locally convex spaces important in applications,” In:Proc. of Voronezh semin. on functional analysis, Vol. 5 (1957), pp. 22–34.
D. Ramachandran, “Existence of independent complements in regular conditional probability spaces,”Ann. Probab.,7, 433–443 (1979).
D. Ramachandran, “Perfect mixtures of perfect measures,”Ann. Probab.,7, No. 3, 444–452 (1979).
D. Ramachandran, “A note on regular conditional probabilities in Doob's sense,”Ann. Probab.,9, No. 5, 907–908 (1981).
D. Ramachandran, “Perfect measures. Pt. I. Basic theory,”ISI Lecture Notes,5, Macmillan Co. of India, Ltd., New Delhi (1979).
D. Ramachandran, “Perfect measures. Pt. II. Special topics,”ISI Lecture Notes,7, Macmillan Co. of India, Ltd., New Delhi (1979).
M. M. Rao,Measure Theory and Integration, John Wiley & Sons, Inc., New York (1987).
M. M. Rao,Conditional Measures and Applications, Marcel Dekker, Inc., New York (1993).
M. M. Rao and V. V. Sazonov, “A theorem on a projective limit of probability spaces and its applications,”Theor. Probab. Appl.,38, No. 2, 345–355 (1993).
R. R. Rao, “Relations between weak and uniform convergences of measures with applications,”Ann. Math. Statist.,18, 659–680 (1962).
M. Remy, “Disintegration and perfectness of measure spaces,”Manuscripta Math.,62, No. 3, 277–296 (1988).
P. Ressel, “Some continuity and measurability results on spaces of measures,”Math. Scand.,40, 69–78 (1977).
M. A. Rieffel, “The Radon-Nikodym theorem for the Rochner integral,”Trans. Amer. Math. Soc.,131, 466–487 (1968).
E. A. Riss,Measures Which Agree on Small Balls. I, II [in Russian], Preprint Kursk Pedagogical Institute, Kursk (1989).
V. A. Rokhlin, “On the fundamental ideas of measure theory,”Mat. Sb. (N.S.),25 (67), 107–150 (1949); English translation:Amer. Math. Soc. Transl.,71 (1952).
B. Rodriguez-Salinas, “Quasi-Radon measures and Radon measures of type (H),”Rend. Circ. Mat. Palermo (2),40, No. 1, 142–152 (1991).
B. Rodriguez-Salinas and P. Jimenez-Guerra, “Radon measures of type (H) in arbitrary topological spaces,”Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid,10 (1979).
B. Rodriguez-Salinas, “Strictly localizable measures,”Rend. Circ. Mat. Palermo (2),41, No. 2, 295–301 (1992).
C. A. Rogers,Hausdorff Measures, Cambridge Univ. Press (1970).
C. A. Rogers, “A linear Borel set whose difference set is not a Borel set,”Bull. London Math. Soc.,2, 41–42 (1970).
C. A. Rogers, “Analytic sets,” In:Proc. Symp. London Math. Soc., Academic Press, New York (1981).
C. A. Rogers and J. E. Jayne, “K-analytic sets,” In:Analytic Sets, Academic Press, New York (1980), pp. 1–181.
L. Rogge, “The convergence determining class of regular open sets,”Proc. Amer. Math. Soc.,37, 581–585 (1973).
J. Rosinski, “On the convolution of cylindrical measures,”Bull. Acad. Polon. Sci., Sér. Sci. Math.,30, Nos. 7–8, 379–383 (1982).
K. Ross and K. Stromberg, “Baire sets and Baire measures,”Ark. Mat.,6, 151–160 (1965).
G. Royer, “Comparaison des mesures de Cauchy en dimension infinie,”Z. Wahrsch. Verw. Geb. 64, No. 1, 7–14 (1983).
Th. De La Rue, “Espaces de Lebesgue,”Lect. Notes Math.,1557, 15–21 (1993).
C. Ryll-Nardzewski, “On quasi-compact measures,”Fund. Math.,40, 125–130 (1953).
J. Saint-Pierre, “Désintegration d'une mesure non borné,”Ann. Inst. H. Poincaré, Sect. B,11, No. 3, 275–286 (1975).
M. Sakai, “Nowhere densely generated properties in topological measure theory,”Tsukuba J. Math.,10, No. 1, 73–77 (1986).
S. Saks,Theory of the Integral, Warszawa (1937).
A. Sapounakis, “The existence of strong liftings for totally ordered measure spaces,”Pacif. J. Math.,106, No. 1, 145–151 (1983).
H. Sato, “Banach support of a probability measure in a locally convex space,”Lect. Notes Math.,526, 221–226 (1976).
H. Sato, “Hilbertian support of a probability measure on a Banach space,”Lect. Notes Math.,709, 195–205 (1979).
A. N. Sazhenkov, “A uniform boundedness principle for topological measures,”Mat. Zametki,31, No. 2, 263–267 (1982).
V. V. Sazonov, “A remark on characteristic functionals,”Theor. Probab. Appl.,3, 201–205 (1968).
V. V. Sazonov, “On perfect measures,”Izv. Akad. Nauk SSSR, Ser. Mat.,26, No. 3, 391–414 (1962); English translation:Amer. Math. Soc. Transl. (2)48, 229–254 (1965).
V. V. Sazonov and V. N. Tutubalin, “Probability distributions on topological groups,”Theor. Probab. Appl.,11, No. 1, 3–55 (1966).
W. Schachermayer, “Mesures cylindriques sur les espaces de Banach, qui ont la propriété de Radon-Nikodym,”C.R. Acad. Sci. Paris, Sér., A,282, 227–229 (1976).
W. Schachermayer, “Eberlein-compacta et espaces de Radon,”C.R. Acad. Sci. Paris, Sér. A-B,284, No. 7, A405-A407 (1977).
W. Schachermayer, “Measurable and continuous linear functionals on spaces of uniformly continuous functions,”Lect. Notes Math.,945, 155–166 (1982).
H. H. Schaefer,Topological Vector Spaces, Springer-Verlag, Berlin-New York (1971).
A. Schief, “The continuity of subtraction and the Hausdorff property in spaces of Borel measures,”Math. Scand.,63, No. 2, 215–219 (1988).
A. Schief, “Topological properties of the addition map in spaces of Borel measures,”Math. Ann.,282, No. 1, 23–31 (1988).
A. Schief, “On continuous image averaging of Borel measures,”Topol. Appl.,31, No. 3, 309–315 (1989).
A. Schief, “An open mapping theorem for measures,”Monatsh. Math.,108, No. 1, 59–70 (1989).
J. Schmets, “Espaces de fonctions continues,”Lect. Notes Math.,519 (1976).
L. Schwartz,Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford Univ. Press, London (1973).
L. Schwartz, “Surmartingales régulières à valeurs mesures et désintégrations régulières d'une mesure,”J. Analyse Math., 26, 1–168 (1973).
L. Schwartz, “Certaines propriétés des mesures sur les espaces de Banach, Seminaire Maurey-Schwartz” (1975–1976). Exposé 23, Centre Math., École Polytech., Palaiseau (1976).
L. Schwartz,Disintegration of Measures, Tata Institute of Fundamental Research, Bombay (1976).
L. Schwartz, “Calculs stochastiques directs sur les trajectoires et propriétés de boreliens porteurs,”Lect. Notes Math.,1059, 271–326 (1984).
L. Schwartz, “Geometry and probability in Banach spaces,”Lect. Notes Math.,852 (1981).
W. Seidel, “Supports of Borel measures,”Fund. Math.,133, No. 1, 67–80 (1989).
F. D. Sentilles, “Compact ness and convergence in the space of measures,”Illinois J. Math.,13, 761–768 (1969).
F. D. Sentilles, “Bounded continuous functions on a completely regular space,”Trans. Amer. Math. Soc.,168, 311–336 (1972).
R. Shutz, “On regular and sigma-smooth two-valued measures and lattice generated topologies,”Internat. J. Math. Sci.,16, No. 1, 33–40 (1993).
D. Siegel, “Outer measures and weak regularity of measures,”Internat. J. Math. Math. Sci.,18, No. 1, 49–58 (1995).
M. Sion, “On capacitability and measurability,”Ann. Inst. Fourier (Grenoble),13, 88–99 (1963).
M. Sion, “Cylinder measures, local bases and nuclearity,”Lect. Notes. Math.,1206, 259–280 (1986).
H. J. Skala, “The existence of probability measures with given marginals,”Ann. Probab.,21, No. 1, 136–142 (1993).
A. V. Skorohod, “Limit theorems for stochastic processes,”Theor. Probab. Appl.,1, 161–290, (1956).
A. V. Skorohod,Integration in Hilbert Space, Springer-Verlag, Berlin-New York (1974).
W. Slowikowski, “Fonctionelles linéaires dans des réunions dénombrables d'espaces de Banach réflexifs,”C.R. Acad. Sci. Paris,262, A870-A872 (1966).
W. Slowikowski, “Pre-supports of linear probability measures and linear Lusin measurable functionals,”Dissert. Math.,93, 1–43 (1972).
W. Smolenski, “Pre-supports and kernels of probability measures in Fréchet spaces,”Demonstratio Math.,10, 751–762 (1977).
W. Smolenski, “An abstract form of a counterexample of Marek Kanter,”Lect. Notes Math.,1080, 288–291 (1984).
W. Smolenski, “On the approximation of measurable linear, functionals,”Statist. Probab. Lett.,3, No. 4, 205–207 (1985).
O. G. Smolyanov, “Measurable linear varieties in products of linear spaces with measure,”Mat. Zametki,5, 623–634 (1969).
O. G. Smolyanov, “The Gross-Sazonov theorem for sign-variable cylindrical measures,”Moscow Univ. Math. Bull.,38, 1–9 (1983).
O. G. Smolyanov and S. V. Fomin, “Measures on topological linear spaces,”Russian Math. Surveys,31, 1–53 (1976).
O. G. Smolyanov and E. T. Shavgulidze, “A simple proof of Tarieladze's theorem on the sufficiency of positive-definite topologies,”Theor. Probab. Appl.,37, No. 2, 421–424 (1992).
A. D. Sokal, “Existence of compatible families of proper regular conditional probabilities,”Z. Wahr. theor. verw. Geb.,56, No. 4, 537–548 (1981).
R. Solovay, “Real-valued measurable cardinals”, In:Axiomatic Set Theory (Proc. Synapos. Pure Math., Vol. XIII, Pt. I), pp. 397–428.Amer. Math. Soc., Providence, R.I. (1971).
D. Sondermann, “Masse auf lokalbeschränkten Räumen,”Ann. Inst. Fourier,19, No. 2, 33–113 (1969).
M. Souslin, “Sur une définition des ensembles mesurables B sans nombres transfinis,”C.R. Acad. Sci. Paris,164, No. 2, 89–91 (1917).
E. Sparre Andersen and B. Jenssen, “On the introduction of measures in infinite product sets,”Danske Vid. Selsk. Math.-Fys. Medd.,25, No. 4 (1948).
M. Startek and D. Szynal, “On a metric defined on the space of probability measures,”Riv. Mat. Univ. Parma (4),15, 219–226 (1989).
L. Steen and J. Seebach,Counterexamples in Topology, Springer, New York (1978) (second ed.).
C. Stegall, “The topology of certain spaces of measures,”Topol. Appl.,41, No. 1-2, 73–112 (1991).
J. D. Stein, “A uniform boundedness theorem for measures,”Michigan Math. J.,19, No. 2, 161–165 (1972).
A. H. Stone, “Topology and measure theory,”Lect. Notes Math.,541, 43–48 (1976).
V. Strassen, “The existence of probability measures with given marginals,”Ann. Math. Statist.,36, 423–439 (1965).
V. N. Sudakov, “Geometric problems of the theory of infinite-dimensional probability distributions,”Tr. Mat. Inst. Steklov,141, 1–190 (1976); English translation:Proc. Steklov Inst. Math., No. 2, 1–178 (1979).
A. Sultan, “A general measure extension procedure,”Proc. Amer. Math. Soc.,69, 37–45 (1978).
C. Sunyach, “Une charactérisation des espaces universellement Radon mesurables,”C.R. Acad. Sci. Paris,268, 864–866 (1969).
Y. Takahashi, “On the relation between Radonifying mappings and kernels of probability measures on Banach spaces,”Hokkaido Math. J.,14, No. 1, 97–106 (1985).
Y. Takahashi and Y. Okazaki, “0–1 laws of a probability measure on a locally convex space,”Publ. Res. Inst. Math. Sci.,22, No. 1, 97–102 (1986).
M. Talagrand, “Hyperplans universallement mesurables,”C.R. Acad. Sci. Paris, Sér. A,291, A501-A502 (1980).
M. Talagrand, “Separabilité vague dans l'espace des mesures sur un compact,”Israel J. Math.,37, 171–180 (1980).
M. Talagrand, “La τ-régularité des mesures gaussiennes,”Z. Wahrsch. und verw. Geb.,57, No. 2, 213–221 (1981).
M. Talagrand, “Pettis integral and measure theory,”Memoirs Amer. Math. Soc.,51, No. 307, 1–224 (1984).
R. Talamo, “Ultrafilters, classes of ideals and measure theory,”Rend. Circ. Mat. Palermo (2), Suppl. No. 4, 115–132 (1984).
F. D. Tall, “Applying set theory to measure theory,”Lect. Notes Math.,1033, 295–302 (1983).
V. I. Tarieladze, “Characteristic functionals and cylindrical measures in DS-groups,” In:Probability theory and Mathematical Statistics, Vol. II (Vilnius, 1985), VNU Sci. Press, Utrecht (1987), pp. 625–648.
V. I. Tarieladze, “On topological description of characteristic functionals,”Dokl. Akad. Nauk SSSR,295, No. 6, 1320–1323 (1987).
V. I. Tarieladze, “Topological description of characteristic functionals on certain groups,”Theor. Probab. Appl.,34, No. 4, 719–730 (1989).
F. Topsøe, “Preservation of weak convergence under mappings,”Ann. Math. Statist.,38, No. 6, 1661–1665 (1967).
F. Topsoe, “A criterion for weak convergence of measures with an application to convergence of measures onD[0, 1],”Math. Scand.,25, 97–104 (1969).
F. Topsøe, “Topology and measure,”Lect. Notes Math.,133 (1970).
F. Topsøe, “Compactness in spaces of measures,”Studia Math.,36, 195–212 (1970).
F. Topsøe, “Compactness and tightness in a space of measures with the topology of weak convergence,”Math. Scand.,34, 187–210 (1974).
F. Topsøe, “Some special results on convergent sequences of Radon measures,”Manuscripta Math.,19, 1–14 (1976).
F. Topsøe, “Further results on integral representations,”Studia Math.,55, 239–245 (1976).
F. Topsøe, “Uniformity in weak convergence with respect to balls in Banach spaces,”Math. Scand.,38, 148–158 (1976).
F. Topsøe, “On construction of measures,” In:Proc. of the Conf. Topology and Measure I (Zinnowitz, 1974), pt. 2, Ernst-Moritz-Arndt Universitat, Greifswald (1978), pp. 343–381.
F. Topsøe, “Approximating pavings and construction of measures,”Colloq. Math.,42, 377–385 (1979).
F. Topsøe, “Radon measures, some basic constructions,”Lect. Notes Math.,1033, 303–311 (1983).
F. Topsøe, “The Souslin operation in topology and measure theory, selected topics,” In:Proc. of the Conf. Topology and Measure III. Pt. 1, 2. J. Flachsmeyer, Z. Frolik, Ju.M. Smirnov, F. Topsoe, and F. Terpe, eds., Ernst-Moritz-Arndt Universitat, Greifswald (1982), pp. 283–312.
F. Topsøe and J. Hoffmann-Jorgensen, “Analytic spaces and their applications,” In:Analytic sets, Proc. Symp. London Math. Soc., Academic Press, New York (1980), pp. 317–403.
A. Tortrat, “Loise(λ) dans les espaces vectoriels et lois stables,”Z. Wahr. theor. verw. Geb.,37, No. 2, 175–182 (1976).
A. Tortrat, “τ-Regularité des lois, séparation au sens de A. Tulcea et propriété de Radon-Nikodym,”Ann. Inst. H. Poincaré Sect. B (N.S.),12, No. 2, 131–150 (1976); Addendum, ibid.13, 43 (1977).
A. Tortrat, “Prolongements τ-réguliers. Applications aux probabilités gaussiennes,”Symposia Math.,21, 117–138 (1977).
B. S. Tsirelson, “A natural modification of a random process, and its application to series of random functions and to Gaussian measures,”Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI),55, 35–63 (1976); Supplement to: “A natural modification of a random process and its application to series of random functions and to Gaussian measures,”Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI)72, 202–211 (1977); English translation:J. Sov. Math.,16, 940–956 (1981).
T. Traynor, “An elementary proof of the lifting theorem,”Pacif. J. Math.,53, No. 1, 267–272 (1974).
S. Ulam, “Zur Masstheorie in der allgemeinen Mengenlehre,”Fund. Math.,16, 140–150 (1930).
K. Urbanik, “Random linear functionals and random integrals,”Colloq. Math.,38, No. 2, 255–263 (1975).
N. N. Vakhania and V. I. Tarieladze, “Covariance operators of probability measures in locally convex spaces,”Theor. Probab. Appl.,23, 3–26 (1978).
N. N. Vakhania, V. I. Tarieladze, and S. A. Chobanyan,Probability Distributions in Banach Spaces, Kluwer Acad. Publ. (1991).
M. Valadier, “Désintégration d'une mesure sur un produit,”C.R. Acad. Sci. Paris A-B,276, A33-A35 (1973).
M. Valdivia, “On Suslin locally convex spaces,”Rev. Real Acad. Cienc. Exact. Fis. Natur. Madrid,72, No. 2, 215–220 (1978).
J. A. van Casteren, “Strictly positive Radon measures,”J. London Math. Soc. (2),49, No. 1, 109–123 (1994).
V. S. Varadarajan, “Measures on topological spaces,”Mat. Sb. (N.S.),55 (97), 35–100 (1961); English translation:Amer. Math. Soc. Transl. (2)48, 161–228 (1965).
A. M. Vershik and V. N. Sudakov, “Probability measures in infinite-dimensional spaces,”Zap. Nauchn. Sem. LOMI,12, 7–67 (1969); English translation:Seminars in Math.,12, 1–28 (1971).
V. G. Vinokurov, “Compact measures and products of Lebesgue spaces,”Mat. Sb. (N.S.),74 (116), 434–472 (1967).
D. A. Vladimirov,Boolean Algebras [in Russian], Nauka, Moscow (1969).
M. L. Wage, “The dimension of product spaces,”Proc. Natl. Acad. Sci. USA,75, No. 10, 4671–4672 (1978).
M. L. Wage, “The product of Radon spaces,”Usp. Mat. Nauk,35, No. 3, 151–153 (1980); English translation:Russian Math. Surveys,35, 185–187 (1980).
D. Wagner, “Survey of measurable selection theorems: an update,”Lect. Notes Math.,794, 119–184 (1980).
B. B. Wells, Jr., “Weak compactness of measures,”Proc. Amer. Soc.,20, 124–134 (1969).
R. Wheeler, “Topological measure theory for completely regular spaces and their projective covers,”Pacif. J. Math.,82, 565–584 (1979).
R. Wheeler, “Extehsions of a σ-additive measure to the projective cover,”Lect. Notes Math.,794, 81–104 (1980).
R. F. Wheeler, “A survey of Baire measures and strict topologies,”Exposition. Math.,1, No. 2, 97–190 (1983).
M. J. Wichura, “On the construction of almost uniformly convergent random variables with given weakly convergent image laws,”Ann. Math. Statist.,41, No. 1, 284–291 (1970).
M. J. Wichura, “A note on the weak convergence of stochastic processes,”Ann. Math. Statist.,42, No. 5, 1769–1772 (1971).
R. J. Wilson, “Weak convergence of probability measures in spaces of smooth functions,”Stochastic Process. Appl.,23, No. 2, 333–337 (1986).
G. L. Wise and E. B. Hall,Counterexamples in Probability and Real Analysis, Oxford Univ. Press (1994).
A. Wisniewski, “Theorem of Kuratowski-Suslin for measurable mappings,”Proc. Amer. Math. Soc.,123, No. 5, 1475–1479 (1995).
W. A. Woyczynski, “Geometry and martingales in Banach spaces. Pt. II: independent increments,”Adv. Prob., Dekker, New York,4, 267–517 (1978).
N. N. Yakovlev, “On biocompacta in Σ-products and related spaces,”Commun. Math. Univ. Carol.,21, 263–282 (1980).
S. Yu. Zholkov, “On Radon spaces,”Dokl. Akad. Nauk SSSR,262, No. 4, 787–790 (1982); English translation:Sov. Math. Dokl.,25, No. 1, 113–117 (1982).
R. E. Zink, “On the structure of measure spaces,”Acta Math.,107, 53–71 (1962).
W. Adamski, “On extremal extensions of regular contents and measures,”Proc. Amer. Math. Soc.,121, No. 4, 1159–1164 (1994).
S. Argyros, “On compact spaces without strictly positive measures,”Pacif. J. Math.,105, No. 2, 257–272 (1983).
W. W. Comfort and S. Negrepontis,Chain condition in topology, Cambridige, Cambridge University Press (1982).
M. Dzamonja and K. Kunen, “Properties of the class of measure separable compact spaces,”Fund. Math.,147, 261–277 (1995).
H. W. Ellis, “Darboux properties and applications to non-absolutely convergent integrals,”Canad. J. Math.,3, 471–485 (1951).
D. Fremlin, “Measure algebras,”, In:Handbook of Boolean Algebras, J. D. Monk, ed., V. 3, North-Holland (1989), pp. 877–980.
D. Fremlin, “Real-valued-measurable cardinals,” In:Set theory of the reals (Ramat Gan, 1991), Israel Math. Conf. Proc. 6, Bar Ilan Univ., Ramat Gan (1993), pp. 151–304.
S. Grekas, “Measure-theoretic problems in topological dynamics,”J. Anal. Math.,65, 207–220 (1995).
A. B. Kharazishvili, “On separable supports of Borel measures,”Georgian Math. J.,2, No. 1, 45–53 (1995).
G. Plebanek, “On Radon measures on first-countable spaces,”Fund. Math.,148, 159–164 (1995).
H. Rademacher, “Eineindeutige Abbildungen und Meßbarkeit,”Monatsh. für Mathematik und Physik,27, 183–290 (1916).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 36. Functional Analysis-1. 1996.
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Bogachev, V.I. Measures on topological spaces. J Math Sci 91, 3033–3156 (1998). https://doi.org/10.1007/BF02432851
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DOI: https://doi.org/10.1007/BF02432851