Completely positive entropy
= Completely positive entropy
{title2=CPE}
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.