Even Kakutani Equivalence And The Loose Block Independence Property For Positive Entropy Zᵈ Actions

Authors

Aimee S. A. Johnson, Swarthmore CollegeFollow
A. A. Şahin

Document Type

Article

Publication Date

Summer 2001

Published In

Illinois Journal Of Mathematics

Abstract

In this paper we define the loose block independence property for positive entropy Zᵈ 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 Zᵈ actions are also loose block independent.

Comments

This work is freely available courtesy of the Department of Mathematics at University of Illinois at Urbana-Champaign.

Recommended Citation

Aimee S. A. Johnson and A. A. Şahin. (2001). "Even Kakutani Equivalence And The Loose Block Independence Property For Positive Entropy Zᵈ Actions". Illinois Journal Of Mathematics. Volume 45, Issue 2. 495-516.
https://works.swarthmore.edu/fac-math-stat/69