{
  "id": "1309.3094",
  "version": "v1",
  "published": "2013-09-12T10:14:41.000Z",
  "updated": "2013-09-12T10:14:41.000Z",
  "title": "Luzin's Condition (N) and Modulus of Continuity",
  "authors": [
    "Pekka Koskela",
    "Jan Malý",
    "Thomas Zürcher"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we establish Luzin's condition (N) for mappings in certain Sobolev-Orlicz spaces with certain moduli of continuity. Further, given a mapping in these Sobolev-Orlicz spaces, we give bounds on the size of the exceptional set where Luzin's condition (N) may fail. If a mapping violates Luzin's condition (N), we show that there is a Cantor set of measure zero that is mapped to a set of positive measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-12T10:14:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B15",
      "26B35",
      "46E35"
    ],
    "keywords": [
      "continuity",
      "sobolev-orlicz spaces",
      "mapping violates luzins condition",
      "exceptional set",
      "cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3094K"
    }
  }
}