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Nonsingular Bernoulli
actions of arbitrary Krieger type
Tey Berendschot and Stefaan Vaes |
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Vol. 15 (2022), No. 5, 1313–1373
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Abstract |
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We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type II and type III. We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions with arbitrary base space , both for amenable and for nonamenable groups. Earlier work focused on two-point base spaces , where type II was proven not to occur. |
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Keywords
nonsingular Bernoulli action, Krieger type, type-III
action, nonsingular ergodic theory
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Mathematical Subject Classification
Primary: 28D15, 37A40
Secondary: 37A15, 37A20, 46L36
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Milestones
Received: 17 June 2020
Revised: 5 January 2021
Accepted: 10 February 2021
Published: 29 September 2022
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Authors |
| Tey Berendschot | |
| Department of Mathematics KU Leuven Leuven Belgium |
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| Stefaan Vaes | |
| Department of Mathematics KU Leuven Leuven Belgium |
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