Kolmogorov's law of the iterated logarithm for Banach space valued random variables

Abstract

Kolmogorov's version of the law of the iterated logarithm (LIL) for random variables taking values in a real separable Banach space is established. This result has several corollaries dealing with the LIL for independent, identically distributed (i.i.d.) sequences and, in particular, extends some of the recent work of G. Pisier.