English

Continuous and Random Vapnik-Chervonenkis Classes

Logic 2010-04-22 v1

Abstract

We show that if TT is a dependent theory then so is its Keisler randomisation TRT^R. In order to do this we generalise the notion of a Vapnik-Chervonenkis class to families of [0,1][0,1]-valued functions (a \emph{continuous} Vapnik-Chervonenkis class), and we characterise families of functions having this property via the growth rate of the mean width of an associated family of convex compacts.

Keywords

Cite

@article{arxiv.0802.0068,
  title  = {Continuous and Random Vapnik-Chervonenkis Classes},
  author = {Itaï Ben Yaacov},
  journal= {arXiv preprint arXiv:0802.0068},
  year   = {2010}
}
R2 v1 2026-06-21T10:08:35.917Z