{
  "id": "0912.2210",
  "version": "v1",
  "published": "2009-12-11T12:12:30.000Z",
  "updated": "2009-12-11T12:12:30.000Z",
  "title": "On Measure Invariance for a 2-valued Transformation",
  "authors": [
    "P. I. Troshin"
  ],
  "comment": "15 pages, 5 figures",
  "journal": "P.I. Troshin. On measure invariance for a 2-valued transformation. Uchenye zapiski Kazanskogo universiteta. Ser. Phys.-math. nauki, vol. 151, no. 4 (2009), pp. 183-191, ISSN 1815-6088",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We consider a family S=S(a) of 2-valued transformations of special form on the segment [0,1] with measure $\\mu=\\int p(x) d\\lambda$, which is absolutely continuous with respect to the Lebesgue measure $\\lambda$. We endow S with a set of weight functions $\\alpha=\\{\\alpha_1(x),\\alpha_2(x)\\}$ and find a criterion of measure invariance under the transformation. This criterion relates the three parameters $a$, $p$, $\\alpha$ to each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-11T12:12:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28D05",
      "37A05",
      "37E05"
    ],
    "keywords": [
      "measure invariance",
      "transformation",
      "criterion relates",
      "special form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.2210T"
    }
  }
}