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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Loosely Bernoulli Cartesian products
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by Laif Swanson PDF
Proc. Amer. Math. Soc. 73 (1979), 73-78 Request permission

Abstract:

For any totally ergodic loosely Bernoulli automorphism T, a class $\mathcal {S}(T)$ of loosely Bernoulli automorphisms is constructed. Each class $\mathcal {S}(T)$ includes zero entropy automorphisms which do not have discrete spectrum, and has the property that for $S \in \mathcal {S}(T)$, the Cartesian product $T \times S$ is loosely Bernoulli.
References
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  • Shizuo Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635–641. MR 14222
  • A. B. Katok, Time change, monotone equivalence, and standard dynamical systems, Dokl. Akad. Nauk SSSR 223 (1975), no. 4, 789–792 (Russian). MR 0412383
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  • D. Rudolph, Nonequivalence of measure preserving transformations, Lecture Notes, 1976. —, If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli (to appear). B. Weiss, Equivalence of measure preserving transformations, Lecture Notes, The Institute for Advanced Studies of the Hebrew University of Jerusalem, 1976.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 73 (1979), 73-78
  • MSC: Primary 28D20
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0512061-9
  • MathSciNet review: 512061