Submission date: 16 February 2015.

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.

Mathematics Subject Classification: 03C45 52C99

Keywords and phrases:

Full text arXiv 1502.04513: pdf, ps.