{
  "id": "0811.0109",
  "version": "v1",
  "published": "2008-11-01T19:30:07.000Z",
  "updated": "2008-11-01T19:30:07.000Z",
  "title": "Stability of invariant measures",
  "authors": [
    "Sinisa Slijepcevic"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and it also differs from topologies induced by the Riesz Representation Theorem. It turns out that the constructed topology is a solution of a limit case of a $p$-optimal transport problem, for $p=\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-01T19:30:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B25"
    ],
    "keywords": [
      "invariant measures",
      "optimal transport problem",
      "riesz representation theorem",
      "limit case",
      "invariant sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.0109S"
    }
  }
}