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EVERY COUNTABLE GROUP HAS THE WEAK ROHLIN PROPERTY

Published online by Cambridge University Press:  19 December 2006

E. GLASNER
Affiliation:
Department of Mathematics, Tel Aviv University, Ramat Aviv, Israelglasner@math.tau.ac.il
J.-P. THOUVENOT
Affiliation:
Laboratoire de Probabilités, Université Paris VI, Paris, Francekalikow@ccr.jussieu.fr
B. WEISS
Affiliation:
Mathematics Institute, Hebrew University of Jerusalem, Jerusalem, Israelweiss@math.huji.ac.il
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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.

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Type
Papers
Copyright
The London Mathematical Society 2006

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