{
  "id": "2111.15469",
  "version": "v2",
  "published": "2021-11-30T15:07:35.000Z",
  "updated": "2022-04-08T10:56:31.000Z",
  "title": "A Strong Law of Large Numbers for Positive Random Variables",
  "authors": [
    "Ioannis Karatzas",
    "Walter Schachermayer"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In the spirit of the famous KOML\\'OS (1967) theorem, every sequence of nonnegative, measurable functions $\\{ f_n \\}_{n \\in \\N}$ on a probability space, contains a subsequence which - along with all its subsequences - converges a.e. in CES\\`ARO mean to some measurable $f_* : \\Omega \\to [0, \\infty]$. This result of VON WEIZS\\\"ACKER (2004) is proved here using a new methodology and elementary tools; these sharpen also a theorem of DELBAEN & SCHACHERMAYER (1994), replacing general convex combinations by CES\\`ARO means.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-08T10:56:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60A10",
      "60F15"
    ],
    "keywords": [
      "positive random variables",
      "large numbers",
      "strong law",
      "replacing general convex combinations",
      "subsequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}