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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.