{
  "id": "1405.2401",
  "version": "v1",
  "published": "2014-05-10T06:49:58.000Z",
  "updated": "2014-05-10T06:49:58.000Z",
  "title": "On the Construction and the Cardinality of Finite $σ$-Fields",
  "authors": [
    "P. Vellaisamy",
    "S. Ghosh",
    "M. Sreehari"
  ],
  "comment": "16 pages. Journal of Analysis (2012)",
  "journal": "Journal of Analysis, 20 (2012), 103-119",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note, we first discuss some properties of generated $\\sigma$-fields and a simple approach to the construction of finite $\\sigma$-fields. It is shown that the $\\sigma$-field generated by a finite class of $\\sigma$-distinct sets which are also atoms, is the same as the one generated by the partition induced by them. The range of the cardinality of such a generated $\\sigma$-field is explicitly obtained. Some typical examples and their complete forms are discussed. We discuss also a simple algorithm to find the exact cardinality of some particular finite $\\sigma$-fields. Finally, an application of our results to statistics, with regard to independence of events, is pointed out.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-10T06:49:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A05",
      "60A05"
    ],
    "keywords": [
      "construction",
      "simple approach",
      "exact cardinality",
      "distinct sets",
      "complete forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2401V"
    }
  }
}