EVERY COUNTABLE GROUP HAS THE WEAK ROHLIN PROPERTY

Abstract

We present a simple proof of the fact that every countable group ${\Gamma}$ is weak Rohlin, that is, there is in the Polish space $mathbb{A}_{\Gamma}$ of measure preserving ${\Gamma}$-actions an action $\mathbf{T}$ whose orbit in $\mathbb{A}_{\Gamma}$ under conjugations is dense. In conjunction with earlier results this in turn yields a new characterization of non-Kazhdan groups as those groups which admit such an action $\mathbf{T}$ which is also ergodic.