Entropy, dimension and the Elton-Pajor Theorem
Skip to main content
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

Entropy, dimension and the Elton-Pajor Theorem

  • Author(s): Mendelson, S
  • Vershynin, R
  • et al.
Creative Commons 'BY' version 4.0 license

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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View