Nonsingular Bernoulli actions of arbitrary Krieger type

Berendschot, Tey; Vaes, Stefaan

doi:10.2140/apde.2022.15.1313

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Nonsingular Bernoulli actions of arbitrary Krieger type

Tey Berendschot and Stefaan Vaes

Vol. 15 (2022), No. 5, 1313–1373

DOI: 10.2140/apde.2022.15.1313

Abstract

We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type II $_{\infty}$ and type III $_{0}$ . We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions $G ↷ \prod_{g \in G} (X_{0}, μ_{g})$ with arbitrary base space $X_{0}$ , both for amenable and for nonamenable groups. Earlier work focused on two-point base spaces $X_{0} = {0, 1}$ , where type II $_{\infty}$ was proven not to occur.

Keywords

nonsingular Bernoulli action, Krieger type, type-III action, nonsingular ergodic theory

Mathematical Subject Classification

Primary: 28D15, 37A40

Secondary: 37A15, 37A20, 46L36

Milestones

Received: 17 June 2020

Revised: 5 January 2021

Accepted: 10 February 2021

Published: 29 September 2022

Authors

Tey Berendschot
Department of Mathematics KU Leuven Leuven Belgium

Stefaan Vaes
Department of Mathematics KU Leuven Leuven Belgium

Vol. 15, No. 5, 2022