A counterexample concerning uniform ergodic theorems for a class of functions
type: Item
instance of: scholarly article
title: A counterexample concerning uniform ergodic theorems for a class of functions
zbMATH Open document ID: 0835.60025
DOI: 10.1016/0167-7152(94)00163-3
published in: Statistics \& Probability Letters
publication date: 1996-03-26T00:00:00Z
review text: It is proved that \textit{V. N. Vapnik}'s and \textit{A. Ya. Chervonenkis}' [Theory Probab. Appl. 16, 264-280 (1971); translation from Teor. Veroyatn. Primen. 16, 264-279 (1971; Zbl 0247.60005)] and \textit{M. Talagrand}'s [Ann. Probab. 15, 837-870 (1987; Zbl 0632.60024)] conditions do not imply convergence of relative frequencies to the probability \(P(C)\) for every set \(C \in {\mathcal L} \subset {\mathcal F}\) if one replaces the sequence of independent random variables with values in measurable space \(({\mathcal X}, {\mathcal F})\) by an ergodic stationary random process defined on \(({\mathcal X}, {\mathcal F})\) with marginal distribution \(P\).
reviewed by: Nijolė Kalinauskaitė
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G10
zbMATH DE Number: 796377
zbMATH Keywords: Glivenko-Cantelli class
zbMATH Keywords: Vapnik-Chervonenkis class
zbMATH Keywords: stationary ergodic processes
author: Andrew B. Nobel
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)00163-3
OpenAlex ID: W2008335039
Wikidata QID: Q125019311
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description: scientific article; zbMATH DE number 796377