论文标题
在某些通用类别的千古措施中保存转换
On some generic classes of ergodic measure preserving transformations
论文作者
论文摘要
我们积极回答了Ryzhikov的问题，即，我们表明，作为一个相对较弱的混合扩展是波兰保存转换的措施群体中的一项稳定属性。我们研究一些相关的千古转换及其相互关系。在本文的第二部分中，我们表明，对于带有属性A的固定的恒星t，t的通用扩展$ \ hat {t} $也具有属性A。在此处，每个属性都有一个立场：（i）具有与t，（ii）bernoulli，（iii）K，（iii）K和（iv）loosely bernoulli相同的熵。
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 with property A, a generic extension $\hat{T}$ of T also has the property A. Here A stands for each of the following properties: (i) having the same entropy as T, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli.
