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Amenable Invariant Random Subgroups

Abstract : We show that an amenable Invariant Random Subgroup of a locally compact second countable group lives in the amenable radical. This answers a question raised in the introduction of the paper "Kesten's Theorem for Invariant Random Subgroup" by Abert, Glasner and Virag. We also consider, in the opposite direction, property (T), and prove a similar statement for this property. The Appendix by Phillip Wesolek proves that the set of amenable subgroups is a Borel subset in the Chabauty topology.
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Jean Lécureux, Uri Bader, Bruno Duchesne, Jean Lecureux, Phillip Wesolek. Amenable Invariant Random Subgroups. Israël Journal of Mathematics, Hebrew University Magnes Press, 2016, 213 (1), pp.399-422. ⟨10.1007/s11856-016-1324-7⟩. ⟨hal-01064474v3⟩



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