{
  "id": "1410.6125",
  "version": "v1",
  "published": "2014-10-22T18:15:23.000Z",
  "updated": "2014-10-22T18:15:23.000Z",
  "title": "Profile decomposition for sequences of Borel measures",
  "authors": [
    "Mihai Mariş"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP",
    "math.CA",
    "math.FA"
  ],
  "abstract": "We prove that, if dichotomy occurs when the concentration-compactness principle is used, the dichotomizing sequence can be choosen so that a nontrivial part of it concentrates. Iterating this argument leads to a profile decomposition for arbitrary sequences of bounded Borel measures. To illustrate our results we give an application to the structure of bouded sequences in the Sobolev space $ W^{1, p}(\\R^N)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-22T18:15:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "profile decomposition",
      "dichotomy occurs",
      "bounded borel measures",
      "arbitrary sequences",
      "concentration-compactness principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6125M"
    }
  }
}