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arXiv · 2101.04967

When all points are generic for ergodic measures

Tomasz Downarowicz·Benjamin Weiss
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Abstract

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 Cesaro means of every continuous function converge uniformly.

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Tomasz Downarowicz, Benjamin Weiss. 2021-01-13. When all points are generic for ergodic measures. https://arxiv.org/abs/2101.04967

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