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 $\sum_{n=1}^{\infty}x_{n}$.
@article{119301,
author = {Juan Carlos Ferrando},
title = {On the convergence of certain sums of independent random elements},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {77-81},
zbl = {1090.46009},
mrnumber = {1903308},
language = {en},
url = {http://dml.mathdoc.fr/item/119301}
}
Ferrando, Juan Carlos. On the convergence of certain sums of independent random elements. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 77-81. http://gdmltest.u-ga.fr/item/119301/
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