{
  "id": "2011.05584",
  "version": "v1",
  "published": "2020-11-11T06:15:24.000Z",
  "updated": "2020-11-11T06:15:24.000Z",
  "title": "An elementary construction of the Wiener measure",
  "authors": [
    "R. P. Pakshirajan",
    "M. Sreehari"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Our construction of the Wiener measure on $\\mathfrak{C}$ consists in first defining a set function $\\varphi$\\ on the class of all compact sets based on certain $n$-dimensional normal distributions, $n = 1,\\ 2,\\ldots$\\ using the structural relation at (1) below. This structural relation, discovered by the first author, is recorded in his book [2] on page 130. We then define a measure $\\mu$ on the Borel $\\sigma$-field of subsets of $\\textbf{C}$ which is the Wiener measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-11T06:15:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60G15"
    ],
    "keywords": [
      "wiener measure",
      "elementary construction",
      "structural relation",
      "dimensional normal distributions",
      "set function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}