Continuous and Random Vapnik-Chervonenkis Classes

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.

References in corpus (1)

• Continuous first order logic and local stability

Cited by in corpus (4)

• On theories of random variables
• Isometry group of Borel randomizations
• Generic Stability and Modes of Convergence
• Glivenko-Cantelli classes and NIP formulas