International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 381-384

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

Rohan Hemasinha

University of West Florida, Pensacola 32514, FL, USA

Received 4 August 1989; Revised 21 March 1990

Copyright © 1991 Rohan Hemasinha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let E be a Banach space, and let (Ω,,P) be a probability space. If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(Ω)(1P<), 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.