Abstract
We give an elementary proof for Lewis Bowen’s theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and every free product Γ of infinite amenable groups, the factor Γ↷KΓ/K of the Bernoulli action Γ↷KΓ by the diagonal K-action is isomorphic with a Bernoulli action of Γ.
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