 Completely positive entropy

A probability measure-preserving system has completely positive entropy if $h_{\mu }(T,\xi )>0$ for every finite measurable partition with $H_{\mu }(\xi )>0$. Equivalently, its Pinsker sigma-algebra is trivial. Since finite partitions measurable in a partition tail have zero entropy rate, this property forces every finite-partition tail sigma-algebra of a measurable partition to be trivial.