{
  "id": "1805.06919",
  "version": "v1",
  "published": "2018-05-17T18:33:03.000Z",
  "updated": "2018-05-17T18:33:03.000Z",
  "title": "Luzin-type properties and the difference quotient of a real function",
  "authors": [
    "Yuri Andreev",
    "Trevor J Richards"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We introduce the notion of the difference quotient set of a real valued function $f$ on a set $E\\subset[0,1]$, and compare this set to the range of $f$ on $E$. We discuss the measure theoretic properties of both the range and the difference quotient set of $f$ over $E$ under different assumptions on $f$ and $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-17T18:33:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A99"
    ],
    "keywords": [
      "real function",
      "luzin-type properties",
      "difference quotient set",
      "measure theoretic properties",
      "real valued function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}