{
  "id": "1404.7454",
  "version": "v2",
  "published": "2014-04-27T14:12:39.000Z",
  "updated": "2015-08-12T19:29:03.000Z",
  "title": "Marcinkiewicz-Zygmund Strong Law of Large Numbers for Pairwise i.i.d. Random Variables",
  "authors": [
    "Valery Korchevsky"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "It is shown that the Marcinkiewicz-Zygmund strong law of large numbers holds for pairwise independent identically distributed random variables. It is proved that if $X_{1}, X_{2}, \\ldots$ are pairwise independent identically distributed random variables such that $E|X_{1}|^p < \\infty$ for some $1 < p < 2$, then $(S_{n}-ES_{n})/n^{1/p} \\to 0$ a.s. where $S_{n} = \\sum_{k=1}^{n} X_{k}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-27T14:12:39.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-12T19:29:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15"
    ],
    "keywords": [
      "marcinkiewicz-zygmund strong law",
      "large numbers",
      "independent identically distributed random variables",
      "pairwise independent identically distributed random"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.7454K"
    }
  }
}