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
Recommended Citation
Godbole, A.
(1987).
On the strong law of large numbers in banach spaces.
Proceedings of the American Mathematical Society,
100(3), 543-550.
http://doi.org/10.1090/S0002-9939-1987-0891161-2
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/9761
