Bernoulli actions are weakly contained in any free action

Miklós Abért; Benjamin Weiss

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arXiv · 1103.1063

Bernoulli actions are weakly contained in any free action

Miklós Abért·Benjamin Weiss

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Abstract

We show that for any countable group, any free probability measure preserving action of the group weakly contains all Bernoulli actions of the group. It follows that for a finitely generated groups, the cost is maximal on Bernoulli actions and that all free factors of i.i.d.-s the group have the same cost. We also show that if a probability measure preserving action f is ergodic, but not strongly ergodic, then f is weakly equivalent to f\timesI where I denotes the trivial action on the unit interval. This leads to a relative version of the Glasner-Weiss dichotomy.

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Miklós Abért, Benjamin Weiss. 2011-09-27. Bernoulli actions are weakly contained in any free action. https://arxiv.org/abs/1103.1063

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