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

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.