Continuous and Random Vapnik-Chervonenkis Classes
Yaacov, Itaï Ben
Original · EN
We show that if T is a dependent theory then so is its Keisler randomisation Tʳ. In order to do this we generalise the notion of a Vapnik-Chervonenkis class to families of [0,1]-valued functions (a 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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