2016/04/04 by Adams, Terrence M.
#28D05 (secondary) #37A25 (primary) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1604.01090
For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is positive. In particular, we give a straightforward proof that any mildly mixing transformation T has a dense algebra C such that T is lightly mixing on C. Also, we provide a hierarchy for the properties of lightly mixing, sweeping out and uniform sweeping out for dense collections, and dense algebras of sets. As a result, stronger mixing realizations are given for several types of transformations than those given by previous extensions of the Jewett-Krieger Theorem.