{
  "id": "1702.01142",
  "version": "v1",
  "published": "2017-02-03T20:03:28.000Z",
  "updated": "2017-02-03T20:03:28.000Z",
  "title": "Measure extension by local approximation",
  "authors": [
    "Iosif Pinelis"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned sense if and only if it is Carath\\'eodory-measurable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-03T20:03:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A12",
      "60A10"
    ],
    "keywords": [
      "local approximation",
      "corresponding measure extension theorem",
      "mentioned sense",
      "measurable sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}