English

VC-sets and generic compact domination

Logic 2016-01-27 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.1502.04513,
  title  = {VC-sets and generic compact domination},
  author = {Pierre Simon},
  journal= {arXiv preprint arXiv:1502.04513},
  year   = {2016}
}

Comments

15 pages

R2 v1 2026-06-22T08:30:25.045Z