arXiv:math/0201048 Abstract

arXiv:math/0201048 [math.FA]Abstract References Reviews Resources

Entropy, dimension and the Elton-Pajor Theorem

Published 2002-01-07Version 1

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.

Categories: math.FA, math.CO

Keywords: elton-pajor theorem, uniform central limit theorem, convex body governs, optimal eltons theorem, coordinate cube

Related articles:

arXiv:math/0203275 [math.FA] (Published 2002-03-26, updated 2002-09-25)

Entropy and the Combinatorial Dimension

S. Mendelson, R. Vershynin

arXiv:math/0404192 [math.FA] (Published 2004-04-08)

Combinatorics of random processes and sections of convex bodies

Mark Rudelson, Roman Vershynin