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arXiv · 1507.05357

Weak containment rigidity for distal actions

Adrian Ioana·Robin Tucker-Drob
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Abstract

We prove that if a measure distal action $\alpha$ of a countable group $\Gamma$ is weakly contained in a strongly ergodic probability measure preserving action $\beta$ of $\Gamma$, then $\alpha$ is a factor of $\beta$. In particular, this applies when $\alpha$ is a compact action. As a consequence, we show that the weak equivalence class of any strongly ergodic action completely remembers the weak isomorphism class of the maximal distal factor arising in the Furstenberg-Zimmer Structure Theorem.

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Adrian Ioana, Robin Tucker-Drob. 2015-07-20. Weak containment rigidity for distal actions. https://arxiv.org/abs/1507.05357

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