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
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 be a Banach space, and let be a probability space.
If contains an isomorphic copy of then in , the closed
linear span of every sequence of independent, valued mean zero random variables has
infinite codimension. If is reflexive or -convex and then the closed
linear span of any family of independent, valued, mean zero random
variables is super-reflexive.