On the convergence of certain sums of independent random elements
Commentationes Mathematicae Universitatis Carolinae (2002)
- Volume: 43, Issue: 1, page 77-81
- ISSN: 0010-2628
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topFerrando, Juan Carlos. "On the convergence of certain sums of independent random elements." Commentationes Mathematicae Universitatis Carolinae 43.1 (2002): 77-81. <http://eudml.org/doc/248962>.
@article{Ferrando2002,
abstract = {In this note we investigate the relationship between the convergence of the sequence $\lbrace S_\{n\}\rbrace $ 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 $i\in \mathbb \{N\}$) and the existence of certain weakly unconditionally Cauchy subseries of $\sum _\{n=1\}^\{\infty \}x_\{n\}$.},
author = {Ferrando, Juan Carlos},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {independent random elements; copy of $c_\{0\}$; Pettis integrable function; perfect measure space; independent random elements; copy of ; Pettis integrable function; perfect measure space},
language = {eng},
number = {1},
pages = {77-81},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the convergence of certain sums of independent random elements},
url = {http://eudml.org/doc/248962},
volume = {43},
year = {2002},
}
TY - JOUR
AU - Ferrando, Juan Carlos
TI - On the convergence of certain sums of independent random elements
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 1
SP - 77
EP - 81
AB - In this note we investigate the relationship between the convergence of the sequence $\lbrace S_{n}\rbrace $ 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 $i\in \mathbb {N}$) and the existence of certain weakly unconditionally Cauchy subseries of $\sum _{n=1}^{\infty }x_{n}$.
LA - eng
KW - independent random elements; copy of $c_{0}$; Pettis integrable function; perfect measure space; independent random elements; copy of ; Pettis integrable function; perfect measure space
UR - http://eudml.org/doc/248962
ER -
References
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