{
  "id": "1705.03584",
  "version": "v1",
  "published": "2017-05-10T02:21:03.000Z",
  "updated": "2017-05-10T02:21:03.000Z",
  "title": "Lectures on the mean values of functionals -- An elementary introduction to infinite-dimensional probability",
  "authors": [
    "Cheng-shi Liu"
  ],
  "comment": "57",
  "categories": [
    "math.PR",
    "math-ph",
    "math.FA",
    "math.MP",
    "math.ST",
    "physics.comp-ph",
    "stat.TH"
  ],
  "abstract": "This is an elementary introduction to infinite-dimensional probability. In the lectures, we compute the exact mean values of some functionals on C[0,1] and L[0,1] by considering these functionals as infinite-dimensional random variables. The results show that there exist the complete concentration of measure phenomenon for these mean values since the variances are all zeroes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-10T02:21:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elementary introduction",
      "infinite-dimensional probability",
      "functionals",
      "exact mean values",
      "infinite-dimensional random variables"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}