{
  "id": "1402.6364",
  "version": "v1",
  "published": "2014-02-25T22:20:54.000Z",
  "updated": "2014-02-25T22:20:54.000Z",
  "title": "The Topology of Information on the Space of Probability Measures over Product of Polish Spaces",
  "authors": [
    "Martin Barbie",
    "Abhishek Gupta"
  ],
  "comment": "30 pages, submitted to Journal of Mathematical Economics",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We study here the topology of information on the space of probability measures over Polish spaces that was defined in Hellwig (1996). 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. This also corrects the proof of a claim in Hellwig (1996, Lemma 4). Additionally, we determine sufficient conditions on the Polish spaces and the topology over measures spaces under which a convergent sequence of probability measures is also convergent in the topology of information.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-25T22:20:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "polish spaces",
      "information",
      "conditional independence property converges",
      "convergent sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6364B"
    }
  }
}