#### 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${}_{\infty }$ and type III${}_{0}$. We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions $G↷{\prod }_{g\in G}\left({X}_{0},{\mu }_{g}\right)$ with arbitrary base space ${X}_{0}$, both for amenable and for nonamenable groups. Earlier work focused on two-point base spaces ${X}_{0}=\left\{0,1\right\}$, 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