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arXiv · 1705.02947

Validity space of Dunford-Schwartz pointwise ergodic theorem

Vladimir Chilin·Semyon Litvinov
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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 $f\in \mathcal L^1(Ω)+\mathcal L^{\infty}(Ω)$ if and only if $μ\{f\ge λ\}<\infty$ for all $λ>0$.

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Vladimir Chilin, Semyon Litvinov. 2017-05-08. Validity space of Dunford-Schwartz pointwise ergodic theorem. https://arxiv.org/abs/1705.02947

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