Nonsingular Bernoulli actions of arbitrary Krieger type

Abstract

We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type $I{I}_{\infty }$ and type $II{I}_0$. We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions $G\curvearrowright {\prod }_{g\in G}(X_0,{\mu }_g)$ 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 $I{I}_{\infty }$ was proven not to occur.

v3: minor revisions, final version, to appear in Analysis and PDE

References in corpus (1)

• Ergodicity and type of nonsingular Bernoulli actions

Cited by in corpus (2)

• Some factors of nonsingular Bernoulli shifts
• Bernoulli actions of type III${}_0$ with prescribed associated flow