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

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 Følner sequence. For a given characteristic class, we prove that the set of points that are generic (along the Følner sequence) for some measure in this class is closed with respect to the Besicovitch pseudometric.

12 pages