{
  "id": "1406.4950",
  "version": "v1",
  "published": "2014-06-19T05:45:37.000Z",
  "updated": "2014-06-19T05:45:37.000Z",
  "title": "On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p",
  "authors": [
    "S. Astashkin",
    "F. Sukochev",
    "D. Zanin"
  ],
  "comment": "14 pages, submitted",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let 1\\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span l_M in L_p is essentially unique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-19T05:45:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46B20",
      "46B09"
    ],
    "keywords": [
      "independent copies span",
      "distribution",
      "uniqueness",
      "orlicz sequence space",
      "mean zero random variable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.4950A"
    }
  }
}