The validity space of Dunford–Schwartz pointwise ergodic theorem

Vladimir Chilin; Semyon Litvinov

doi:10.1016/j.jmaa.2018.01.001

The validity space of Dunford–Schwartz pointwise ergodic theorem

Vladimir Chilin, Semyon Litvinov

Penn State Hazleton

Research output: Contribution to journal › Article › peer-review

5 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 language	English (US)
Pages (from-to)	234-247
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	461
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.01.001
State	Published - May 1 2018

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2018.01.001

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title = "The validity space of Dunford–Schwartz pointwise ergodic theorem",

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.",

author = "Vladimir Chilin and Semyon Litvinov",

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AU - Litvinov, Semyon

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N2 - 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.

AB - 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.

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

The validity space of Dunford–Schwartz pointwise ergodic theorem

Abstract

All Science Journal Classification (ASJC) codes

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