The validity space of Dunford–Schwartz pointwise ergodic theorem

Vladimir Chilin, Semyon Litvinov

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We show that if a σ-finite infinite measure space (Ω,μ) is quasi-non-atomic, then the Dunford–Schwartz pointwise ergodic theorem holds for f∈L1(Ω)+L(Ω) if and only if μ{|f|≥λ}<∞ for all λ>0.

Original languageEnglish (US)
Pages (from-to)234-247
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume461
Issue number1
DOIs
StatePublished - May 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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