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A note on the almost sure limiting behavior of the maximum of a sequence of partial sums. (English) Zbl 0691.60024

Summary: The goal of this paper is to show that, in most strong laws of large numbers, the n th partial sum can be replaced with the largest of the first n sums. Moreover, it is shown that the usual assumptions of independence and common distribution are unnecessary and that these results also apply to strong laws for Banach valued random elements.

MSC:

60F15 Strong limit theorems
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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