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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the strong law of large numbers in Banach spaces
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by Anant P. Godbole PDF
Proc. Amer. Math. Soc. 100 (1987), 543-550 Request permission

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 are the best possible of their kind and may be used in situations where the SLLN’s of Hoffman-Jørgensen and Pisier, and Kuelbs and Zinn are inconclusive.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 100 (1987), 543-550
  • MSC: Primary 60B11; Secondary 46B20, 60B12
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0891161-2
  • MathSciNet review: 891161