On the strong law of large numbers in banach spaces

Document Type

Article

Publication Date

1-1-1987

Abstract

We study the relationship between the geometry of a real separable Banach space B (as manifested in its cotype, type, or logtype) and necessary or sufficient criteria for the validity of the Strong Law of Large Numbers (SLLN) for independent B-valued random variables, formulated in terms of the validity of a (verifiable) SLLN for real-valued random variables. Our results axe the best possible of their kind and may be used in situations where the SLLN's of Hoffman-Jorgensen and Pisier, and Kuelbs and Zinn are inconclusive. © 1987 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society

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