{
  "id": "1307.3989",
  "version": "v3",
  "published": "2013-07-15T15:26:08.000Z",
  "updated": "2014-02-22T21:33:30.000Z",
  "title": "The Topology of Information on the Space of Probability Measures over Polish Spaces",
  "authors": [
    "Abhishek Gupta"
  ],
  "comment": "Some proofs have been modified/elaborated and the paper has been expanded. Please see the new paper for correct proofs and more results on this topology",
  "categories": [
    "math.PR",
    "math.FA",
    "math.OC"
  ],
  "abstract": "We study here the topology of information on the space of probability measures over Polish spaces that was defined in [1]. We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence property converges to a measure that also satisfies the same conditional independence property. In the process of showing this, we also provide a correct proof of the result in Lemma 4 in [1].",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-02-22T21:33:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "polish spaces",
      "information",
      "conditional independence property converges",
      "convergent sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3989G"
    }
  }
}