Mean Distality and Tightness

摘要

A relationship between the entropy invaxiant and a certain property of topological dynamical systems with a finite invariant measure μ is studied. This property means that, after removing a μ-null set, there are no distinct mean proximal points in the system (a pair x, y is mean proximal with respect to a homeomorphism T of a compact metric space with a metric d if lim 1/(2n+1) ∑_(-n)~n d(T~ix, T~iy) = 0).