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arXiv · 0802.0068

Continuous and Random Vapnik-Chervonenkis Classes

Itaï Ben Yaacov
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Abstract

We show that if $T$ is a dependent theory then so is its Keisler randomisation $T^R$. In order to do this we generalise the notion of a Vapnik-Chervonenkis class to families of $[0,1]$-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.

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BibTeXRIS

Itaï Ben Yaacov. 2008-02-01. Continuous and Random Vapnik-Chervonenkis Classes. https://doi.org/10.1007/s11856-009-0094-x

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