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Positive entropy actions of countable groups factor onto Bernoulli shifts
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We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory.
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Cited by 1 Pith paper
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Positive Rokhlin Entropy Implies Infinite $L^1$-Orbit Multiplicity: A Negative Answer to Thouvenot's Question
Free ergodic amenable actions with positive Rokhlin entropy have infinite complex L1- and L10-orbit multiplicity, so no finite family of functions has dense Koopman orbit span.
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