On almost symmetric sequences in \(L_ p\)
type: Item
instance of: scholarly article
title: On almost symmetric sequences in \(L_ p\)
zbMATH Open document ID: 0704.60024
DOI: 10.1007/BF01952057
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: The sequence \((X_ n)\) of random variables is said to be K-symmetric in \(L_ p\) if E \(| X_ n|^ p\) is finite for any \(n=1,2,..\). and \[ K^{-1}\| a_ 1X_ 1+...+a_ nX_ n\|_ p\leq \| a_ 1X_{b(1)}+...+a_ nX_{b(n)}\|_ p\leq K\| a_ 1X_ 1+...+a_ nX_ n\|_ p \] for every \(n=1,2,...\), \((a_ 1,...,a_ n)\in R^ n\) and any permutation (b(1),...,b(n)) of (1,...,n). The sequence \((X_ n)\) is almost symmetric in \(L_ p\) if for any \(a>0\) there exists an \(N=N(a)\) such that \((X_ n)_{n>N}\) is \((1+a)\)- symmetric in \(L_ p.\) A characterization of almost symmetric subsequences of \((X_ n)\) is given.
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4155559
zbMATH Keywords: symmetric sequences
zbMATH Keywords: characterization of almost symmetric subsequences
author: István Berkes
reviewed by: Svetlozar T. Rachev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01952057
OpenAlex ID: W2046464378
description: scientific article; zbMATH DE number 4155559