VC-sets and generic compact domination
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Let X be a closed subset of a locally compact second countable group G whose family of translates has finite VC-dimension. We show that the topological border of X has Haar measure 0. Under an extra technical hypothesis, this also holds if X is constructible. We deduce from this generic compact domination for definably amenable NIP groups.
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- [CS15]A. Chernikov and P. Simon, Definably amenable NIP groups, preprint, 2015.Google Scholar