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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Positive entropy actions of countable groups factor onto Bernoulli shifts
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by Brandon Seward HTML | PDF
J. Amer. Math. Soc. 33 (2020), 57-101 Request permission


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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Additional Information
  • Brandon Seward
  • Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10003
  • MR Author ID: 884743
  • Email:
  • Received by editor(s): April 14, 2018
  • Received by editor(s) in revised form: April 21, 2019, and May 20, 2019
  • Published electronically: September 27, 2019
  • Additional Notes: The author was partially supported by ERC grant 306494 and Simons Foundation grant 328027 (P.I. Tim Austin).
  • © Copyright 2019 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 33 (2020), 57-101
  • MSC (2010): Primary 37A35, 37A15
  • DOI:
  • MathSciNet review: 4066472