Summary
A CLT and a LIL are proved under weak-L 2 Gaussian bracketing conditions (weaker than the usual ones). These results have wide applicability and in particular provide an improvement of the Jain-Marcus central limit theorem for C(S)-valued random variables.
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The research of these authors was carried out while visiting Texas A & M University
The research of these authors has been totally or partially supported by the Danish Natural Science Research Council and by the National Science Foundation Grants numbers DMS-83-18610 and DMS-83-01367
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Andersen, N.T., Giné, E., Ossiander, M. et al. The central limit theorem and the law of iterated logarithm for empirical processes under local conditions. Probab. Th. Rel. Fields 77, 271–305 (1988). https://doi.org/10.1007/BF00334041
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DOI: https://doi.org/10.1007/BF00334041