{
  "id": "1601.04088",
  "version": "v1",
  "published": "2016-01-14T12:55:23.000Z",
  "updated": "2016-01-14T12:55:23.000Z",
  "title": "Calculation of Lebesgue Integrals by Using Uniformly Distributed Sequences in $(0,1)$",
  "authors": [
    "Gogi Pantsulaia",
    "Tengiz Kiria"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "We present the proof of Kolmogorov's strong law of large numbers in particular case and consider its applications for calculations of Lebesgue Integrals by using uniformly distributed sequences in $(0,1)$. We extend the result of C. Baxa and J. Schoi$\\beta$engeier (cf.\\cite{BaxSch2002}, Theorem 1, p. 271) to a bigger set $D \\subset(0,1)^{\\infty}$ of uniformly distributed(in $(0,1)$) sequences strictly containing the set of all sequences of real numbers which can be presented in a form $(\\{\\alpha n\\})_{n \\in {\\bf N}}$ for some irrational numbers $\\alpha$ and for which $\\ell_1^{\\infty}(D)=1$, where $\\ell_1^{\\infty}$ denotes the infinite power of the linear Lebesgue measure $\\ell_1$ in $(0,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-14T12:55:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28C10"
    ],
    "keywords": [
      "uniformly distributed sequences",
      "lebesgue integrals",
      "calculation",
      "kolmogorovs strong law",
      "linear lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}