On some generic classes of ergodic measure preserving transformations

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2020-09-15 DOI:10.1090/mosc/312

E. Glasner, J. Thouvenot, B. Weiss

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引用次数: 9

Abstract

We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic transformations and their interrelations. In the second part of the paper we show that for a fixed ergodic T T with property A \mathbf {A} , a generic extension T ^ \widehat {T} of T T also has property A \mathbf {A} . Here A \mathbf {A} stands for each of the following properties: (i) having the same entropy as T T , (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli.

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关于遍历保测度变换的一些一般类

我们肯定地回答了Ryzhikov的一个问题，即证明了在波兰测度保持变换群中，作为一个相对弱混合扩展是一个可交换性质。我们研究了一些相关的遍历变换类及其相互关系。在论文的第二部分，我们证明了对于具有性质a \mathbf {a}的固定遍历T T, T T的一般扩展T ^ \widehat {T}也具有性质a \mathbf {a}。在这里A \mathbf {A}代表以下每一个属性:(i)与T T具有相同的熵，(ii)伯努利，(iii) K， (iv)松散伯努利。

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.