{
  "id": "math/0201048",
  "version": "v1",
  "published": "2002-01-07T22:16:35.000Z",
  "updated": "2002-01-07T22:16:35.000Z",
  "title": "Entropy, dimension and the Elton-Pajor Theorem",
  "authors": [
    "S. Mendelson",
    "R. Vershynin"
  ],
  "categories": [
    "math.FA",
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-07T22:16:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elton-pajor theorem",
      "uniform central limit theorem",
      "convex body governs",
      "optimal eltons theorem",
      "coordinate cube"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1048M"
    }
  }
}