Weak mixing properties for nonsingular actions

TL;DR

This paper investigates various weak mixing properties of nonsingular group actions, comparing them to measure-preserving cases and analyzing which properties and implications remain valid in the nonsingular setting.

Contribution

It systematically examines weak mixing properties for nonsingular actions and identifies which implications from measure-preserving actions still hold.

Findings

Weak mixing properties coincide in measure-preserving actions.

Certain implications of weak mixing persist in nonsingular actions.

The paper clarifies the relationship between different weak mixing notions in nonsingular dynamics.

Abstract

For a general group G we consider various weak mixing properties of nonsingular actions. In the case where the action is actually measure preserving all these properties coincide, and our purpose here is to check which implications persist in the nonsingular case.