Free minimal actions of countable groups with invariant probability measures

TL;DR

This paper demonstrates that every countable group can act freely and minimally on the Cantor set while preserving an invariant probability measure, expanding understanding of group actions in topological dynamics.

Contribution

It establishes the existence of free minimal actions with invariant measures for all countable groups, a significant advancement in dynamical systems theory.

Findings

Existence of free minimal actions for all countable groups

Construction of actions preserving invariant probability measures

Extension of group action theory to broader classes of groups

Abstract

We prove that for any countable group G there exists a free minimal continuous action of G on the Cantor set admitting an invariant Borel probability measure.