Continuous and random Vapnik-Chervonenkis classes

Itaï Ben Yaacov (1)

1 ICJ - Institut Camille Jordan

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.

Domaines: Logique [math.LO]

Itaï Ben Yaacov. Continuous and random Vapnik-Chervonenkis classes. Israel Journal of Mathematics, 2009, 173, pp.309-333. ⟨10.1007/s11856-009-0094-x⟩. ⟨hal-00226392⟩