{
  "id": "1707.01678",
  "version": "v1",
  "published": "2017-07-06T08:27:36.000Z",
  "updated": "2017-07-06T08:27:36.000Z",
  "title": "The Borel-Cantelli Lemmas for contaminated events, and small maxima",
  "authors": [
    "Guus Balkema"
  ],
  "comment": "5 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a sequence of independent events $E_n$ the sum of the associated zero-one random variables $1_{E_n}$ is almost surely finite or almost surely infinite according as the sum of the probabilities converges or diverges. In this paper the events $E_n$ are contaminated. What can one say about $\\sum1_{D_n}$ when $D_n=E_n\\setminus A_n$ for a sequence of events $A_n$ with vanishing probability? The behaviour depends on the relation between the events $E_n$ and $A_n$ and on the size of the events. We prove a Borel-Cantelli lemma for the contaminated variables and give an application in extreme value theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-06T08:27:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60F20",
      "60E15"
    ],
    "keywords": [
      "borel-cantelli lemma",
      "small maxima",
      "contaminated events",
      "associated zero-one random variables",
      "extreme value theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}