Ergodicity and type of nonsingular Bernoulli actions

  title={Ergodicity and type of nonsingular Bernoulli actions},
  author={Michael Bjorklund and Zemer Kosloff and Stefaan Vaes},
  journal={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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Weak mixing for nonsingular Bernoulli actions of countable amenable groups
  • A. I. Danilenko
  • Mathematics
    Proceedings of the American Mathematical Society
  • 2019
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AN INTRODUCTION TO INFINITE ERGODIC THEORY (Mathematical Surveys and Monographs 50)
By Jon Aaronson: 284 pp., US$79.00, isbn 0 8218 0494 4 (American Mathematical Society, 1997).
An introduction to infinite ergodic theory
Non-singular transformations General ergodic and spectral theorems Transformations with infinite invariant measures Markov maps Recurrent events and similarity of Markov shifts Inner functions