A Rokhlin Lemma for Noninvertible Totally-Ordered Measure-Preserving Dynamical Systems
Abstract
Let (X,F,μ,T) be a not necessarily invertible non-atomic measure-preserving dynamical system where the σ-algebra F is generated by the intervals according to some total order. The main result is that the classical Rokhlin lemma may be adapted to such a situation assuming a slight extension of aperiodicity. This result is compared to previous noninvertible versions of the Rokhlin lemma.
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