Ergodicity via continuity

2018/12/05 by I. V. Podvigin, Ivan Podvigin, Podvigin, Ivan
Mathematics · #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #math.DS #msc:28D05 #msc:37A25 #msc:54C05

paper · pdf · doi:10.48550/arxiv.1812.02077

arxiv created 2018/12/05 · arxiv updated 2018/12/06

Abstract

We show that the ergodicity of an aperiodic automorphism of a Lebesgue space is equivalent to the continuity of a certain map on a metric Boolean algebra. A related characterization is also presented for periodic and totally ergodic transformations

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