{
  "id": "1510.02236",
  "version": "v1",
  "published": "2015-10-08T08:44:03.000Z",
  "updated": "2015-10-08T08:44:03.000Z",
  "title": "An Erd\\\" os-R\\' enyi law for nonconventional sums",
  "authors": [
    "Yuri Kifer"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We obtain rge Erd\\\" os-R\\' enyi type law of large numbers for \"nonconventional\" sums of the form $S_n=\\sum^n_{m=1}F(X_m,X_{2m},...,X_{\\ell m})$ where $X_1,X_2,...$ is a sequence of i.i.d. random variables and $F$ is a bounded Borel function. The proof relies on nonconventional large deviations obtained in [8].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-08T08:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15"
    ],
    "keywords": [
      "nonconventional sums",
      "enyi law",
      "enyi type law",
      "nonconventional large deviations",
      "random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151002236K"
    }
  }
}