Article PDF
Avoid common mistakes on your manuscript.
References
I. Csiszár, Eine informationstheoretische Ungleichung, und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten,Publ. Math. Inst. Hungar. Acad. Sci. 8 (1963), Ser. A, 85–108.
I. Csiszár, Information-type measures of difference of probability distributions and indirect observations,Studia Sci. Math. Hungar. 2 (1967), 299–318.
M. S. Pinsker,Information and information stability of random variables and processes, Moscow, 1960 (in Russian).
S. Kullback,Information theory and statistics, New York, 1959.
H. Hahn, Über die Integrale des Herrn Hellinger und die Orthogonalinvarianten der quadratischen Formen von unendlich vielen Veränderlichen,Monatsh. Math. Phys. 23 (1912), 161–224.
A. M. Kagan, Towards the theory of Fisher's amount of information,Dokl. Akad. Nauk SSSR 151 (1963), 277–278 (in Russian).
I. Vajda, On the amount of information contained in a sequence of independent observationsKybernetika (Prague)6 (1970), 306–323.
A. Rényi, On the foundations of information theory,Rev. ISI 33 (1965), 1–14.
A. Rényi, On measures of entropy and information,Proc. 4th Berkeley Symp. on Math. Stat. and Prob., Vol. I, Berkeley, 1960, 547–561.
G. H. Hardy, J. E. Littlewood andG. Pólya,Inequalities, Cambridge, 1959.
S. Kullback, A lower bound for discrimination information in terms of variation,IEEE Trans. Information Theory 13 (1967), 126–127.
P. R. Halmos,Measure theory, New York, 1966.
J. L. Doob,Stochastic processes, New York, 1953.
A. Perez, Notions généralisées d'incertitude, d'entropie et d'information du point de vue de la théorie des martingales,Trans. 1st Prague Conf. on Information Theory, Prague, 1957, 193–208.
T. E. Duncan, On the absolute continuity of measuresAnn. Math. Statist. 41 (1970), 30–38.
I. Vajda, Limit theorems for total variation of Cartesian product measures,Studia Sci. Math. Hungar. 6 (1971), 317–333.
S. Kakutani, On equivalence of infinite product measures,Ann. of Math. 49 (1948), 214–226.
J. Hájek, On a property of normal distributions of an arbitrary stochastic process,Czechoslovak Math. J. 8 (1958), 610–618.
I. Vajda, Note on discrimination information and variation,IEEE Trans. Information Theory 16 (1970), 771–773.
Author information
Authors and Affiliations
Additional information
To the memory of A. Rényi
Rights and permissions
About this article
Cite this article
Vajda, I. On thef-divergence and singularity of probability measures. Period Math Hung 2, 223–234 (1972). https://doi.org/10.1007/BF02018663
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02018663