{
  "id": "math/0506597",
  "version": "v1",
  "published": "2005-06-29T12:08:00.000Z",
  "updated": "2005-06-29T12:08:00.000Z",
  "title": "A strong law of large numbers for capacities",
  "authors": [
    "Fabio Maccheroni",
    "Massimo Marinacci"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117904000001062 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2005, Vol. 33, No. 3, 1171-1178",
  "doi": "10.1214/009117904000001062",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-29T12:08:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A12",
      "60F15"
    ],
    "keywords": [
      "large numbers",
      "strong law",
      "random variables",
      "upper choquet integrals",
      "totally monotone capacity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6597M"
    }
  }
}