Periodic measures are dense in invariant measures for residually finite amenable group actions with specification

TL;DR

This paper proves that for specific group actions with the specification property, periodic measures are dense among invariant measures, enhancing understanding of the structure of invariant measures in such dynamical systems.

Contribution

It establishes the density of periodic measures in invariant measures for residually finite amenable group actions with specification, a significant extension in ergodic theory.

Findings

Periodic measures are dense in invariant measures for the specified actions.

The result applies to actions of residually finite amenable groups.

The proof relies on the specification property of the system.

Abstract

We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.