{
  "id": "1206.2602",
  "version": "v1",
  "published": "2012-06-12T17:36:41.000Z",
  "updated": "2012-06-12T17:36:41.000Z",
  "title": "A new proof for the Banach-Zarecki theorem: A light on integrability and continuity",
  "authors": [
    "Ali Mahdipour-Shirayeh",
    "Homayoon Eshraghi"
  ],
  "comment": "15 pages; Published in the Bulletin of Iranian Mathematical Society, 2012",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "To demonstrate more visibly the close relation between the continuity and integrability, a new proof for the Banach-Zarecki theorem is presented on the basis of the Radon-Nikodym theorem which emphasizes on measure-type properties of the Lebesgue integral. The Banach-Zarecki theorem says that a real-valued function F is absolutely continuous on a finite closed interval if and only if it is continuous and of bounded variation when it satisfies Lusin's condition (N).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-12T17:36:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "46G12"
    ],
    "keywords": [
      "integrability",
      "continuity",
      "satisfies lusins condition",
      "banach-zarecki theorem says",
      "close relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2602M"
    }
  }
}