Bernoulli actions are weakly contained in any free action

Miklós Abért, Benjamin Weiss

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

Let Γ be a countable group and let f be a free probability measure-preserving action of Γ. We show that all Bernoulli actions of Γ are weakly contained in f. It follows that for a finitely generated group Γ, the cost is maximal on Bernoulli actions for Γ and that all free factors of i.i.d. (independent and identically distributed) actions of Γ have the same cost. We also show that if f is ergodic, but not strongly ergodic, then f is weakly equivalent to f×I, where Idenotes the trivial action of Γ on the unit interval. This leads to a relative version of the Glasner-Weiss dichotomy.

Original languageEnglish
Pages (from-to)323-333
Number of pages11
JournalErgodic Theory and Dynamical Systems
Volume33
Issue number2
DOIs
StatePublished - Apr 2013

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