{
  "id": "1403.5413",
  "version": "v2",
  "published": "2014-03-21T10:24:01.000Z",
  "updated": "2015-03-05T19:59:10.000Z",
  "title": "On the existence of the Riemann-Stieltjes integral",
  "authors": [
    "Rafał M. Łochowski"
  ],
  "comment": "More comprehensive paper with the sam results is \"Integration of rough paths - the truncated variation approach, arXiv:1409.3757\"",
  "categories": [
    "math.CA"
  ],
  "abstract": "The purpose of this note is a new proof of Young's theorem on the existence of the Riemann-Stieltjes integral when the integrand and integrator have possibly unbounded variation, but they have finite $p-$variation and $q-$variation respectively, where $p>1,$ $q>1$ and $p^{-1}+q^{-1}>1.$ Our proof will follow easily from a more general theorem formulated in terms of a functional called truncated variation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-21T10:24:01.000Z",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Rafał M. \\Lochowski"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-03-05T19:59:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A42",
      "26A45",
      "34L30"
    ],
    "keywords": [
      "riemann-stieltjes integral",
      "youngs theorem",
      "truncated variation",
      "possibly unbounded variation",
      "general theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5413L"
    }
  }
}