Illinois Journal Of Mathematics
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.
Aimee S. A. Johnson and A. A. Şahin.
"Even Kakutani Equivalence And The Loose Block Independence Property For Positive Entropy Zᵈ Actions".
Illinois Journal Of Mathematics.