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arXiv · 1604.01090

Mixing sets for non-mixing transformations

Terrence M. Adams
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Abstract

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.

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Terrence M. Adams. 2016-04-04. Mixing sets for non-mixing transformations. https://arxiv.org/abs/1604.01090

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