Illinois Journal of Mathematics

Even Kakutani equivalence and the loose block independence property for positive entropy $(\Bbb Z\sp d)$ actions

Aimee S. A. Johnson and Ayşe A. Şahin

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Abstract

In this paper we define the loose block independence property for positive entropy $\mathbb Z^d$ actions and extend some of the classical results to higher dimensions. In particular, we prove that two loose block independent actions are even Kakutani equivalent if and only if they have the same entropy. We also prove that for $d > 1$ the ergodic, isometric extensions of the positive entropy loose block independent $\mathbb Z^d$ actions are also loose block independent.

Article information

Source
Illinois J. Math. Volume 45, Number 2 (2001), 495-516.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138352

Mathematical Reviews number (MathSciNet)
MR1878805

Zentralblatt MATH identifier
1006.37010

Subjects
Primary: 37A35: Entropy and other invariants, isomorphism, classification
Secondary: 28D05: Measure-preserving transformations

Citation

Johnson, Aimee S. A.; Şahin, Ayşe A. Even Kakutani equivalence and the loose block independence property for positive entropy $(\Bbb Z\sp d)$ actions. Illinois J. Math. 45 (2001), no. 2, 495--516. https://projecteuclid.org/euclid.ijm/1258138352.


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