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Hindawi, International Journal of Mathematics and Mathematical Sciences, 2(14), p. 381-384

DOI: 10.1155/s0161171291000443

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

Journal article published in 1991 by Rohan Hemasinha
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Let E be a Banach space, and let (Ω,ℱ,P) be a probability space. If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(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 LEP(Ω)) linear span of any family of independent, E valued, mean zero random variables is super-reflexive.