{
  "id": "1407.2138",
  "version": "v1",
  "published": "2014-07-08T15:42:51.000Z",
  "updated": "2014-07-08T15:42:51.000Z",
  "title": "Differentiation of Integrals",
  "authors": [
    "Shunchao Long"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "No functions class for general measurable sets classes are known whose functions have the property of differentiability of integrals associated to such sets classes. In this paper,we give some subspaces of $L^s$ with $1<s<\\infty$, whose functions are proven to have the differentiability of integrals associated to measurable sets classes in ${\\bf R}^n $, this gives an answer to a question stated by Stein in his book Harmonic Analysis. We give also a example of some functions in these classes on ${\\bf R}^2 $, which is continuous nowhere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-08T15:42:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B35",
      "42B25",
      "26B05",
      "28A15"
    ],
    "keywords": [
      "differentiation",
      "book harmonic analysis",
      "general measurable sets classes",
      "functions class",
      "differentiability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2138L"
    }
  }
}