Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A zero entropy such that the $[T,{\operatorname{Id}}]$ endomorphism is nonstandard

Author(s): Christopher Hoffman
Journal: Proc. Amer. Math. Soc. 128 (2000), 183-188.
MSC (1991): Primary 28D99; Secondary 60A10
Posted: July 1, 1999
MathSciNet review: 1625757
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Abstract | References | Similar articles | Additional information

Abstract: We present an example of an ergodic transformation , a variant of a zero entropy non-loosely Bernoulli map of Feldman, such that the sequence of random variables generated by the [,Id] endomorphism is nonstandard.

References:

1.: J. Feldman. New $K$ -automorphisms and a problem of Kakutani. Israel J. Math. 24 (1976), no. 1, 16-38. MR 53:13515
2.: J. Feldman, D. Rudolph. Standardness of sequences of $\sigma$ -fields given by certain endomorphisms. Fund. Math. 157 (1998), no. 2-3, 175-189. CMP 98:16
3.: D. Heicklen. Bernoullis are standard when entropy is not an obstruction. Israel J. Math. 107 (1998), 141-155. CMP 99:05
4.: D. Heicklen, C. Hoffman. $T$ , $T^{-1}$ is not standard. ETDS. 18 (1998), no. 4, 875-878. CMP 99:01
5.: D. Heicklen, C. Hoffman, D. Rudolph. Entropy and dyadic equivalence of random walks on a random scenery. preprint.
6.: I. Mejilson. Mixing properties of a class of skew-products. Israel J. Math. 19 (1974), 266-270. MR 51:8374
7.: A. M. Vershik. Decreasing sequences of measurable partitions and their applications. Dokl. Akad. Nauk SSSR 193 no. 4 (1970), 748-751. MR 42:3258

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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
Email: hoffman@math.umd.edu

DOI: 10.1090/S0002-9939-99-05057-1
PII: S 0002-9939(99)05057-1
Keywords: Decreasing sequences of $\sigma$-algebras, standard
Received by editor(s): June 17, 1997
Received by editor(s) in revised form: March 13, 1998
Posted: July 1, 1999
Communicated by: Mary Rees
Copyright of article: Copyright 1999, by Christopher Hoffman

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