On the Rokhlin lemma for infinite measure-preserving bijections

TL;DR

This paper extends the Rokhlin lemma to infinite measure-preserving bijections, providing a complete classification up to a specific form of approximate conjugacy, sharpening classical results.

Contribution

It offers a full classification of infinite measure-preserving bijections up to λ-approximate conjugacy, refining the classical Rokhlin lemma's scope.

Findings

Classifies infinite measure-preserving bijections up to λ-approximate conjugacy

Sharpens the classical Rokhlin lemma by strengthening the conjugacy classification

Provides a complete characterization in the infinite measure context

Abstract

We study the Rokhlin lemma in the context of infinite measure-preserving bijections, and completely classify such bijections up to $\lambda$-approximate conjugacy, where $\lambda$ is the infinite measure which is preserved. This sharpens the classical version of the Rokhlin lemma, which only provides such a classification up to $\mu$-approximate conjugacy where $\mu$ is a probability measure equivalent to $\lambda$.