{
  "id": "1606.02848",
  "version": "v1",
  "published": "2016-06-09T07:43:17.000Z",
  "updated": "2016-06-09T07:43:17.000Z",
  "title": "A couple of remarks on the convergence of $σ$-fields on probability spaces",
  "authors": [
    "Matija Vidmar"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "The following modes of convergence of sub-$\\sigma$-fields on a given probability space have been studied in the literature: weak convergence, strong convergence, convergence with respect to the Hausdorff metric, almost-sure convergence, set-theoretic convergence, monotone convergence. It is noted that all preserve independence, and all are invariant under passage to an equivalent probability measure. Partial results for the case of operator-norm convergence obtain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-09T07:43:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60A05",
      "46B28"
    ],
    "keywords": [
      "probability space",
      "equivalent probability measure",
      "operator-norm convergence",
      "weak convergence",
      "strong convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}