# Ergodicity and type of nonsingular Bernoulli actions

@article{Bjorklund2019ErgodicityAT,
title={Ergodicity and type of nonsingular Bernoulli actions},
author={Michael Bjorklund and Zemer Kosloff and Stefaan Vaes},
journal={arXiv: Dynamical Systems},
year={2019}
}
• Published 17 January 2019
• Mathematics
• arXiv: Dynamical Systems
We determine the Krieger type of nonsingular Bernoulli actions $G \curvearrowright \prod_{g \in G} (\{0,1\},\mu_g)$. When $G$ is abelian, we do this for arbitrary marginal measures $\mu_g$. We prove in particular that the action is never of type II$_\infty$ if $G$ is abelian and not locally finite, answering Krengel's question for $G = \mathbb{Z}$. When $G$ is locally finite, we prove that type II$_\infty$ does arise. For arbitrary countable groups, we assume that the marginal measures stay…
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