{
  "id": "1312.6589",
  "version": "v3",
  "published": "2013-12-23T16:24:51.000Z",
  "updated": "2014-10-02T21:15:40.000Z",
  "title": "The linear topology associated with weak convergence of probability measures",
  "authors": [
    "Liang Hong"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by statisticians and our presentation gives an alternative view than most standard probability textbooks. In particular, this functional approach clarifies the underlying topological structure of weak convergence. We hope this short note is helpful for those who are interested in weak convergence as well as instructors of measure theoretic probability.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-29T18:22:45.000Z",
      "abstract": "This exposition note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. We attempt to clarify the underlying linear topological structure of weak convergence. Since this is not a research paper, we claim no novelty; our main task is to collect those results scattered through literature and remove obscurities. We hope this note is helpful for those who are interested in weak convergence but are not familiar with functional analysis (at or beyond the level of topological vector spaces).",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-02T21:15:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "00-01",
      "60F05",
      "60A10"
    ],
    "keywords": [
      "probability measures",
      "linear topology",
      "exposition note aims",
      "underlying linear topological structure",
      "topological vector spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6589H"
    }
  }
}