On the Strong Law of Large Numbers in Banach Spaces
Copyright policy )On the Strong Law of Large Numbers in Banach Spaces
We study the relationship between the geometry of a real separable Banach space B 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 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.
- Michigan Technological University United States
Geometry and structure of normed linear spaces, strong law of large numbers, geometry of a real separable Banach space, Limit theorems for vector-valued random variables (infinite-dimensional case), type p and cotype q Banach spaces
Geometry and structure of normed linear spaces, strong law of large numbers, geometry of a real separable Banach space, Limit theorems for vector-valued random variables (infinite-dimensional case), type p and cotype q Banach spaces
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