Vol. 15, No. 5, 2022

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Nonsingular Bernoulli actions of arbitrary Krieger type

Tey Berendschot and Stefaan Vaes

Vol. 15 (2022), No. 5, 1313–1373
Abstract

We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type II and type III0. We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions G gG(X0,μg) with arbitrary base space X0, both for amenable and for nonamenable groups. Earlier work focused on two-point base spaces X0 = {0,1}, where type II was proven not to occur.

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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