On Rationally Ergodic and Rationally Weakly Mixing Rank-One Transformations

preprint2013arXivOpen access

Abstract

We study the notions of weak rational ergodicity and rational weak mixing as defined by Jon Aaronson. We prove that various families of infinite measure-preserving rank-one transformations possess (or do not posses) these properties, and consider their relation to other notions of mixing in infinite measure.

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