On the pointwise implementation of near-actions

TL;DR

This paper demonstrates that under the continuum hypothesis, every measure-preserving near-action of a group on a standard Borel probability space can be realized pointwise by Borel measure-preserving automorphisms.

Contribution

It establishes a connection between the continuum hypothesis and the pointwise implementation of measure-preserving near-actions.

Findings

Continuum hypothesis implies pointwise implementation of near-actions.

Every measure-preserving near-action has a Borel automorphism realization.

Results are specific to standard Borel probability spaces.

Abstract

We show that the continuum hypothesis implies that every measure preserving near-action of a group on a standard Borel probability space $(X,\mu)$ has a pointwise implementation by Borel measure preserving automorphisms.