{
  "id": "1009.1118",
  "version": "v1",
  "published": "2010-09-06T18:35:16.000Z",
  "updated": "2010-09-06T18:35:16.000Z",
  "title": "A generalized dual maximizer for the Monge--Kantorovich transport problem",
  "authors": [
    "Mathias Beiglböck",
    "Christian Léonard",
    "Walter Schachermayer"
  ],
  "journal": "ESAIM P\\&S 16 (2012) 306-323",
  "categories": [
    "math.OC",
    "math.FA"
  ],
  "abstract": "The dual attainment of the Monge--Kantorovich transport problem is analyzed in a general setting. The spaces $X, Y$ are assumed to be polish and equipped with Borel probability measures $\\mu$ and $\\nu$. The transport cost function $c:\\XY \\to [0,\\infty]$ is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel's perturbation technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-06T18:35:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-kantorovich transport problem",
      "generalized dual maximizer",
      "fenchels perturbation technique",
      "borel probability measures",
      "transport cost function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1118B"
    }
  }
}