VC-sets and generic compact domination

2015/02/16 by Pierre Simon, Simon, Pierre · 1 citation
Mathematics · #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1502.04513

Abstract

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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• Stabilizers and NIP arithmetic regularity

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