VC-sets and generic compact domination
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- Simon, P. Isr. J. Math. (2017) 218: 27. doi:10.1007/s11856-017-1457-3
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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.