{
  "id": "2005.06559",
  "version": "v1",
  "published": "2020-05-13T19:51:13.000Z",
  "updated": "2020-05-13T19:51:13.000Z",
  "title": "Hausdorff measure of critical set for Luzin $N$ condition",
  "authors": [
    "Anna Doležalová",
    "Marika Hrubešová",
    "Tomáš Roskovec"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is well-known that there is a Sobolev homeomorphism $f\\in W^{1,p}([-1,1]^n,[-1,1]^n)$ for any $p<n$ which maps a set $C$ of zero Lebesgue $n$-dimensional measure onto the set of positive measure. We study the size of this critical set $C$ and characterize its lower and upper bounds from the perspective of Hausdorff measures defined by a general gauge function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-13T19:51:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35"
    ],
    "keywords": [
      "hausdorff measure",
      "critical set",
      "general gauge function",
      "dimensional measure",
      "upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}