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Stability of m-equivalence to the weak Pinsker property

Published online by Cambridge University Press:  19 September 2008

Adam Fieldsteel  and
Daniel J. Rudolph
Adam Fieldsteel
Affiliation:
Wesleyan University, Middletown, CT 06457, USA
Daniel J. Rudolph
Affiliation:
University of Maryland, College Park, MD 20742, USA
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Abstract

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Let denote the class of transformations with the weak Pinsker property, and let []m denote the class of transformations m-equivalent to some member of , where m is an entropy-preserving size. We show that if T is a factor of an element of []m, then T ∈ []m, and if T is an m-limit of elements of []m, then T ∈ []m.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 119 - 129
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[1]Ornstein, D. S., Rudolph, D. J. & Benjamin, Weiss. Equivalence of measure preserving transformations. Mem. Amer. Math. Soc. 37 (262) (1982).Google Scholar
[2]Rudolph, D. J.. Restricted orbit equivalence. Mem. Amer. Math. Soc. 54 (323) (1985).Google Scholar
[3]Thouvenot, J. -P.. Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l'un est un schema de Bernoulli. Isr. J. Math. 21 (1975), 177–207.CrossRefGoogle Scholar
[4]Thouvenot, J. -P.. On the stability of the weak Pinsker property. Isr. J. Math. 27 (1977), 150–162.CrossRefGoogle Scholar