, Volume 77, Issue 2, pp 271-305

The central limit theorem and the law of iterated logarithm for empirical processes under local conditions

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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.