The validity space of Dunford-Schwartz ergodic theorem for infinite measure

2017/03/14 by Vladimir Chilin, Chilin, Vladimir, Semyon Litvinov +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1703.04702

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arxiv created 2017/05/08 · arxiv updated 2017/05/09

Abstract

We show that if (Ω,μ) is an infinite measure space, the pointwise Dunford-Shwartz ergodic theorem holds for f ∈ \mathcal L¹(Ω)+\mathcal L^∞(Ω) if and only if μ\f>λ\<∞ for all λ> 0.

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