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Entropy, dimension and the Elton-Pajor Theorem

S. Mendelson·R. Vershynin
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Abstract

The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This has a number of consequences, including the optimal Elton's theorem and a uniform central limit theorem in the real valued case.

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S. Mendelson, R. Vershynin. 2002-01-07. Entropy, dimension and the Elton-Pajor Theorem. https://arxiv.org/abs/math/0201048

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