Validity space of Dunford-Schwartz pointwise ergodic theorem

2017/05/08 by Chilin, Vladimir, Litvinov, Semyon
#37A30(secondary) #47A35(primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1705.02947

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∈ \mathcal L¹(Ω)+\mathcal L^∞(Ω) if and only if μ\f≥ λ\0.

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