Weak containment rigidity for distal actions
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© 2016 Elsevier Inc. We prove that if a measure distal action α of a countable group Γ is weakly contained in a strongly ergodic probability measure preserving action β of Γ, then α is a factor of β. In particular, this applies when α 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.
author list (cited authors)
Ioana, A., & Tucker-Drob, R.