Entropy, dimension and the Elton-Pajor Theorem

Details Entropy, dimension and the Elton-Pajor Theorem Entropy, dimension and the Elton-Pajor Theorem

2002-01-07

arxiv.org/abs/math/0201048v1

Mathematics

Functional Analysis

Scientific paper

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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