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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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A zero entropy $T$ such that the $[T,\!{\operatorname {Id}}]$ endomorphism is nonstandard
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by Christopher Hoffman PDF
Proc. Amer. Math. Soc. 128 (2000), 183-188

Abstract:

We present an example of an ergodic transformation $T$, a variant of a zero entropy non-loosely Bernoulli map of Feldman, such that the sequence of random variables generated by the [$T$,Id] endomorphism is nonstandard.
References
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  • J. Feldman, D. Rudolph. Standardness of sequences of $\sigma$-fields given by certain endomorphisms. Fund. Math. 157 (1998), no. 2–3, 175–189.
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  • D. Heicklen, C. Hoffman. $T$,$T^{-1}$ is not standard. ETDS. 18 (1998), no. 4, 875–878.
  • D. Heicklen, C. Hoffman, D. Rudolph. Entropy and dyadic equivalence of random walks on a random scenery. preprint.
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Additional Information
  • Christopher Hoffman
  • Affiliation: The Hebrew University, Institute of Mathematics, Jerusalem, Israel
  • Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 634876
  • Email: hoffman@math.umd.edu
  • Received by editor(s): June 17, 1997
  • Received by editor(s) in revised form: March 13, 1998
  • Published electronically: July 1, 1999
  • Communicated by: Mary Rees
  • © Copyright 1999 by Christopher Hoffman
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 183-188
  • MSC (1991): Primary 28D99; Secondary 60A10
  • DOI: https://doi.org/10.1090/S0002-9939-99-05057-1
  • MathSciNet review: 1625757