Geodesic
On some generic classes of ergodic measure preserving transformations
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 1, pp. 19-44

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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 $\mathbf{A}$, a generic extension $\widehat{T}$ of $T$ also has the property $\mathbf{A}$. Here $\mathbf{A}$ stands for each of the following properties: (i) having the same entropy as $T$, (ii) Bernoulli, (iii) K, and (iv) loosely Bernoulli. References: 46 entries. 
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     title = {On some generic classes of ergodic measure  preserving transformations},
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E. Glasner; J.-P. Thouvenot; B. Weiss. On some generic classes of ergodic measure  preserving transformations. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 1, pp. 19-44. http://geodesic.mathdoc.fr/item/MMO_2021_82_1_a1/