Generic points in a characteristic class for amenable group actions are closed in the Besicovitch pseudometric

TL;DR

This paper proves that for amenable group actions on compact metric spaces, the set of generic points for measures in a characteristic class forms a closed set under the Besicovitch pseudometric, revealing structural properties of generic points.

Contribution

It establishes the closedness of the set of generic points for measures in a characteristic class in the Besicovitch pseudometric, a new insight into the structure of generic points in amenable group actions.

Findings

The set of generic points for measures in a characteristic class is closed in the Besicovitch pseudometric.

The result applies to actions of countable amenable groups on compact metric spaces.

This provides a new perspective on the topology of generic points in dynamical systems.

Abstract

We consider an action of a countable amenable group on a compact metric space, focusing on the set of generic points with respect to a fixed F{\o}lner sequence. For a given characteristic class, we prove that the set of points that are generic (along the F{\o}lner sequence) for some measure in this class is closed with respect to the Besicovitch pseudometric.