A new proof of the Komlós-Révész-theorem
type: Item
instance of: scholarly article
title: A new proof of the Komlós-Révész-theorem
zbMATH Open document ID: 0701.60022
DOI: 10.1007/BF01197885
publication date: 1990-01-01T00:00:00Z
review text: If r.v.s \(\{X_ n\}\) are given satisfying the moment boundedness condition E \(| X_ n| \leq 1\) then there exists a subsequence \(\bar X_ n=X_{n_ k}\) and a r.v. X with E \(| X| \leq 1\) such that \(n^{-1}\sum^{n}_{i=1}\bar X_ i\to^{a.s.}X.\) This statement has been proved by \textit{P. Révész} [Acta Math. Acad. Sci. Hungar. 16, 311-318 (1965; Zbl 0203.195)] and also by \textit{J. Kolmós} [ibid. 18, 217-229 (1967)]. The author gives a new and simpler proof using some ideas of the theory of orthogonal series and the truncation technique.
reviewed by: Elisaveta Pancheva
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4149254
zbMATH Keywords: a.s. subsequence limit theorem
zbMATH Keywords: truncation technique
author: Rolf Trautner
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01197885
OpenAlex ID: W2911451041
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4149254