Pure strictly uniform models of non-ergodic measure automorphisms

TL;DR

This paper presents a new proof for a stronger version of Hansel's theorem, constructing pure strictly uniform models for non-ergodic measure automorphisms, enhancing control over ergodic measures in the model.

Contribution

It introduces a novel proof that adds the condition of purity to the construction of strictly uniform models for non-ergodic systems.

Findings

Provides a stronger, more controlled model for non-ergodic systems.

Enhances understanding of ergodic measure decomposition.

Strengthens the theoretical framework for measure automorphisms.

Abstract

The classical theorem of Jewett and Krieger gives a strictly ergodic model for any ergodic measure preserving system. An extension of this result for non-ergodic systems was given many years ago by George Hansel. He constructed, for any measure preserving system, a strictly uniform model, i.e. a compact space which admits an upper semicontinuous decomposition into strictly ergodic models of the ergodic components of the measure. In this note we give a new proof of a stronger result by adding the condition of purity, which controls the set of ergodic measures that appear in the strictly uniform model.