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2 Bulletin of the Polish Academy of Sciences. Mathematics

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The ergodic decomposition defined by actions of amenable groups, part II: more about the role played by the ergodic invariant probability measures in the decomposition

Zaharopol Radu

Bulletin of the Polish Academy of Sciences. Mathematics

2021

Vol. 69, no. 1

61--68

Our purpose here is to continue the study of the ergodic decomposition for actions defined by amenable groups, started in [R. Zaharopol, Colloq. Math. 165 (2021)]. We consider the set Γ(w)αcpie defined in the above-mentioned paper, and we prove that it is Borel measurable and of maximal probability.

When all points are generic for ergodic measures

Downarowicz Tomasz, Weiss Benjamin

Bulletin of the Polish Academy of Sciences. Mathematics

2020

Vol. 68, no. 2

117--132

We establish connections between several properties of topological dynamical systems, such as: – every point is generic for an ergodic measure, – the map sending points to the measures they generate is continuous, – the system splits into uniquely (alternatively, strictly) ergodic subsystems, – the map sending ergodic measures to their topological supports is continuous, – the Cesàro means of every continuous function converge uniformly.