Complete metric on mixing actions of general groups

TL;DR

This paper introduces a new metric on the set of mixing actions for countable infinite groups, making the space complete and separable, which advances the understanding of measure-preserving group actions.

Contribution

It defines a complete, separable metric on mixing actions of countable groups, facilitating analysis of their structure and properties.

Findings

The metric space of mixing actions is complete.

The metric space of mixing actions is separable.

Provides a framework for analyzing measure-preserving transformations.

Abstract

In this paper the metric on the set of mixing actions of a countable infinite group is introduced so that the corresponding space is complete and separable. Keywords and phrases. Monotilable group, measure preserving transformations, mixing group actions.