{
  "id": "0803.1244",
  "version": "v2",
  "published": "2008-03-08T14:35:43.000Z",
  "updated": "2008-12-08T11:32:27.000Z",
  "title": "Moments of Two-Variable Functions and the Uniqueness of Graph Limits",
  "authors": [
    "Christian Borgs",
    "Jennifer Chayes",
    "Laszlo Lovasz"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "For a symmetric bounded measurable function W on [0,1]^2, \"moments\" of W can be defined as values t(F,W) indexed by simple graphs. We prove that every such function is determined by its moments up to a measure preserving transformation of the variables. This implies that the limit of a convergent dense graph sequence is unique up to measure preserving transformation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-12-08T11:32:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C99",
      "28A99"
    ],
    "keywords": [
      "graph limits",
      "two-variable functions",
      "measure preserving transformation",
      "uniqueness",
      "convergent dense graph sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1244B"
    }
  }
}