{
  "id": "1502.00694",
  "version": "v1",
  "published": "2015-02-03T00:47:57.000Z",
  "updated": "2015-02-03T00:47:57.000Z",
  "title": "Lusin-type theorems for Cheeger derivatives on metric measure spaces",
  "authors": [
    "Guy C. David"
  ],
  "comment": "16 pages. Comments welcome",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "A theorem of Lusin states that every Borel function on $R$ is equal almost everywhere to the derivative of a continuous function. This result was later generalized to $R^n$ in works of Alberti and Moonens-Pfeffer. In this note, we prove direct analogs of these results on a large class of metric measure spaces, those with doubling measures and Poincar\\'e inequalities, which admit a form of differentiation by a famous theorem of Cheeger.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-03T00:47:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B05",
      "30L99"
    ],
    "keywords": [
      "metric measure spaces",
      "cheeger derivatives",
      "lusin-type theorems",
      "borel function",
      "lusin states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150200694D"
    }
  }
}