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