{
  "id": "1807.07931",
  "version": "v1",
  "published": "2018-07-20T16:41:31.000Z",
  "updated": "2018-07-20T16:41:31.000Z",
  "title": "Equivalence of Uniform and Asymptotic Uniform Integrability Conditions and its Applications",
  "authors": [
    "Eugene A. Feinberg",
    "Pavlo O. Kasyanov",
    "Yan Liang"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "This note establishes the equivalence of uniform and asymptotic uniform integrability conditions for a sequence of functions with respect to a sequence of finite measures. This result is illustrated with new formulations of the Dunford-Pettis theorem, the fundamental theorem for Young measures, and uniform Lebesgue's convergence theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-20T16:41:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic uniform integrability conditions",
      "equivalence",
      "uniform lebesgues convergence theorem",
      "applications",
      "note establishes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}