非可逆全序保测度动力系统的一个Rokhlin引理

IF 0.1 Q4 MATHEMATICS Real Analysis Exchange Pub Date : 2023-10-01 DOI:10.14321/realanalexch.48.2.1645609092

Adam R. B. Erickson

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引用次数: 0

摘要

设$(X,\mathcal{F},\mu,T)$为不一定可逆的非原子保测度动力系统，其中$\sigma$ -代数$\mathcal{F}$是由区间按某种总序生成的。主要的结果是经典的Rokhlin引理可以适用于这种假设非周期性稍微扩展的情况。这个结果与先前的Rokhlin引理的不可逆版本进行了比较。

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A Rokhlin Lemma for Noninvertible Totally-Ordered Measure-Preserving Dynamical Systems

Let $(X,\mathcal{F},\mu,T)$ be a not necessarily invertible non-atomic measure-preserving dynamical system where the $\sigma$-algebra $\mathcal{F}$ 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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