Symmetric spaces and sequences of independent random variables
type: Item
instance of: scholarly article
title: Symmetric spaces and sequences of independent random variables
zbMATH Open document ID: 0601.60005
DOI: 10.1007/BF01077299
publication date: 1985-01-01T00:00:00Z
review text: Let X be a symmetric Banach space on a non-atomic probability space. Let also \((\xi_ n)\) be a sequence of i.i.d. random variables, \(\xi_ n\in X\), which satisfies the following condition: for some \(a,b,c>0\), \(1<q<2\) and all \(x\geq c\) \[ (1)\quad ax^{-q}\leq P[| \xi_ 1| \geq x]\leq bx^{-q}. \] It is announced that if X is perfect or reflexive, then the closed subspace of X generated by \((\xi_ n)\) is isomorphic to \(\ell_ q\). The question of necessity of (1) and the case \(X=L_ p\), \(0<p<1\) are also considered.
Mathematics Subject Classification ID: 60B05
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 3969744
zbMATH Keywords: subspace generated by i.i.d. random variables
zbMATH Keywords: symmetric Banach space
author: Michael Braverman
reviewed by: V. Tarieladze
MaRDI profile type: Publication
cites work: On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
cites work: Rademacher series in symmetric spaces
cites work: Q4188284
full work available at URL: https://doi.org/10.1007/bf01077299
OpenAlex ID: W2099494317
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3969744