J.C. Ferrando
On the convergence of certain sums of independent random elements

Comment.Math.Univ.Carolinae 43,1 (2002) 77-81.

Abstract:In this note we investigate the relationship between the convergence of the sequence $\{S_{n}\}$ of sums of independent random elements of the form $S_{n}=\sum _{i=1}^{n}\varepsilon _{i}x_{i}$ (where $\varepsilon _{i}$ takes the values $\pm 1$ with the same probability and $x_{i}$ belongs to a real Banach space $X$ for each $i\in \Bbb N$) and the existence of certain weakly unconditionally Cauchy subseries of $\sum _{n=1}^{\infty }x_{n}$.

Keywords: independent random elements, copy of $c_{0}$, Pettis integrable function, perfect measure space
AMS Subject Classification: 46B15, 46B09