Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Loosely Bernoulli Cartesian products


Author: Laif Swanson
Journal: Proc. Amer. Math. Soc. 73 (1979), 73-78
MSC: Primary 28D20
MathSciNet review: 512061
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] J. Feldman, New 𝐾-automorphisms and a problem of Kakutani, Israel J. Math. 24 (1976), no. 1, 16–38. MR 0409763 (53 #13515)
  • [2] Shizuo Kakutani, Induced measure preserving transformations, Proc. Imp. Acad. Tokyo 19 (1943), 635–641. MR 0014222 (7,255f)
  • [3] A. B. Katok, Time change, monotone equivalence, and standard dynamical systems, Dokl. Akad. Nauk SSSR 223 (1975), no. 4, 789–792 (Russian). MR 0412383 (54 #509)
  • [4] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspehi Mat. Nauk 22 (1967), no. 5 (137), 81–106 (Russian). MR 0219697 (36 #2776)
  • [5] D. Rudolph, Nonequivalence of measure preserving transformations, Lecture Notes, 1976.
  • [6] -, If a two-point extension of a Bernoulli shift has an ergodic square, then it is Bernoulli (to appear).
  • [7] B. Weiss, Equivalence of measure preserving transformations, Lecture Notes, The Institute for Advanced Studies of the Hebrew University of Jerusalem, 1976.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28D20

Retrieve articles in all journals with MSC: 28D20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0512061-9
PII: S 0002-9939(1979)0512061-9
Keywords: Measure preserving transformations, induced automorphisms, loosely Bernoulli, entropy
Article copyright: © Copyright 1979 American Mathematical Society