Continuous and Random Vapnik-Chervonenkis Classes
Logic
2010-04-22 v1
Abstract
We show that if is a dependent theory then so is its Keisler randomisation . In order to do this we generalise the notion of a Vapnik-Chervonenkis class to families of -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.
Cite
@article{arxiv.0802.0068,
title = {Continuous and Random Vapnik-Chervonenkis Classes},
author = {Itaï Ben Yaacov},
journal= {arXiv preprint arXiv:0802.0068},
year = {2010}
}