On the class of systems which are disjoint from every ergodic system

TL;DR

This paper provides a straightforward proof characterizing measure-preserving systems that are disjoint from all ergodic systems, applicable to any countable group, enhancing understanding of system disjointness in ergodic theory.

Contribution

It offers a direct proof of a recent theorem on disjointness from ergodic systems, extendable to any countable acting group, simplifying previous approaches.

Findings

Characterizes systems disjoint from all ergodic systems

Proof applicable to any countable group

Simplifies understanding of disjointness in ergodic theory

Abstract

In this note we give a fairly direct proof of a recent theorem of Gorska, Lemanczyk and de la Rue which characterises the class of measure preserving transformations that are disjoint from every ergodic measure preserving transformation. Our proof works just as well for any countable acting group.