Positive entropy actions of countable groups factor onto Bernoulli shifts

Brandon Seward

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arXiv · 1804.05269

Positive entropy actions of countable groups factor onto Bernoulli shifts

Brandon Seward

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Abstract

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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Brandon Seward. 2018-04-14. Positive entropy actions of countable groups factor onto Bernoulli shifts. https://arxiv.org/abs/1804.05269

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