Topological groups with Rokhlin properties
Volume 110 / 2008
Colloquium Mathematicum 110 (2008), 51-80
MSC: Primary 22A05; Secondary 37E15, 54C40.
DOI: 10.4064/cm110-1-2
Abstract
In his classical paper [Ann. of Math. 45 (1944)] P. R. Halmos shows that weak mixing is generic in the measure preserving transformations. Later, in his book, Lectures on Ergodic Theory, he gave a more streamlined proof of this fact based on a fundamental lemma due to V. A. Rokhlin. For this reason the name of Rokhlin has been attached to a variety of results, old and new, relating to the density of conjugacy classes in topological groups. In this paper we will survey some of the new developments in this area.
