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arXiv · 2005.06309

Nonsingular Bernoulli actions of arbitrary Krieger type

Tey Berendschot·Stefaan Vaes
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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 $G \curvearrowright \prod_{g \in G} (X_0,μ_g)$ 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.

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Tey Berendschot, Stefaan Vaes. 2021-02-15. Nonsingular Bernoulli actions of arbitrary Krieger type. https://doi.org/10.2140/apde.2022.15.1313

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