Year: 2022
Type: article
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.
DOI: 10.1090/mosc/312
Authors: E. Glasner, J.-P. Thouvenot, B. Weiss
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3085745556