{
  "id": "1908.10655",
  "version": "v1",
  "published": "2019-08-28T11:44:59.000Z",
  "updated": "2019-08-28T11:44:59.000Z",
  "title": "The Lipschitz truncation of functions of bounded variation",
  "authors": [
    "Dominic Breit",
    "Lars Diening",
    "Franz Gmeineder"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct a Lipschitz truncation which approximates functions of bounded variation in the area-strict metric. The Lipschitz truncation changes the original function only on a small set similar to Lusin's theorem. Previous results could only give estimates on the Lebesgue measure of the set where the Lipschitz approximations differ from the original function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-28T11:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "26B35"
    ],
    "keywords": [
      "bounded variation",
      "original function",
      "lipschitz approximations differ",
      "lipschitz truncation changes",
      "small set similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}