Nonrobustness property of the individual ergodic theorem
type: Item
instance of: scholarly article
title: Nonrobustness property of the individual ergodic theorem
zbMATH Open document ID: 1012.37003
DOI: 10.1023/A:1010418008049
published in: Problems of Information Transmission
publication date: 2002-06-03T00:00:00Z
review text: The author proves that Birkhoff's individual ergodic theorem is nonrobust. If the randomness deficiency grows arbitrarily slowly on initial fragments of an infinite sequence, this theorem does not hold. Finally, an analogous nonrobustness property holds for the Shannon-McMillan-Breiman theorem.
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1734723
zbMATH Keywords: individual ergodic theorem
zbMATH Keywords: nonrobustness
zbMATH Keywords: Shannon-McMillan-Breiman theorem
author: Vladimir V. V'yugin
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
full work available at URL: a:1010418008049
OpenAlex ID: W1540433006
description: scientific article; zbMATH DE number 1734723