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Some results on the span of families of Banach valued independent, random variables

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  • Rohan Hemasinha

Abstract

Let E be a Banach space, and let ( Ω , ℱ , P ) be a probability space. If L 1 ( Ω ) contains an isomorphic copy of L 1 [ 0 , 1 ] then in L E P ( Ω ) ( 1 ≤ P < ∞ ) , the closed linear span of every sequence of independent, E valued mean zero random variables has infinite codimension. If E is reflexive or B -convex and 1 < P < ∞ then the closed ( in L E P ( Ω ) ) linear span of any family of independent, E valued, mean zero random variables is super-reflexive.

Suggested Citation

  • Rohan Hemasinha, 1991. "Some results on the span of families of Banach valued independent, random variables," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:861237
    DOI: 10.1155/S0161171291000443
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