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April, 1989 Sums of Independent Random Variables in Rearrangement Invariant Function Spaces
William B. Johnson, G. Schechtman
Ann. Probab. 17(2): 789-808 (April, 1989). DOI: 10.1214/aop/1176991427

Abstract

Let $X$ be a quasinormed rearrangement invariant function space on (0, 1) which contains $L_q(0, 1)$ for some finite $q$. There is an extension of $X$ to a quasinormed rearrangement invariant function space $Y$ on $(0, \infty)$ so that for any sequence $(f_i)^\infty_{i = 1}$ of symmetric random variables on (0,1), the quasinorm of $\sum f_i$ in $X$ is equivalent to the quasinorm of $\sum\mathbf{f}_i$ in $Y$, where $(\mathbf{f}_i)^\infty_{i = 1}$ is a sequence of disjoint functions on $(0, \infty)$ such that for each $i, \mathbf{f}_i$ has the same decreasing rearrangement as $f_i$. When specialized to the case $X = L_q(0, 1)$, this result gives new information on the quantitative local structure of $L_q$.

Citation

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William B. Johnson. G. Schechtman. "Sums of Independent Random Variables in Rearrangement Invariant Function Spaces." Ann. Probab. 17 (2) 789 - 808, April, 1989. https://doi.org/10.1214/aop/1176991427

Information

Published: April, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0674.60051
MathSciNet: MR985390
Digital Object Identifier: 10.1214/aop/1176991427

Subjects:
Primary: 60G50
Secondary: 46E30

Keywords: Independent random variables , Moment inequalities , ‎rearrangement ‎invariant space , Rosenthal's inequality , uniform approximation property

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 2 • April, 1989
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