{
  "id": "1309.2874",
  "version": "v1",
  "published": "2013-09-11T16:09:23.000Z",
  "updated": "2013-09-11T16:09:23.000Z",
  "title": "The $Δ_2$-condition and $\\varphi$-families of probability distributions",
  "authors": [
    "Rui F. Vigelis",
    "Charles C. Cavalcante"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we provide some results related to the $\\Delta_2$-condition of Musielak-Orlicz functions and $\\varphi$-families of probability distributions, which are modeled on Musielak-Orlicz spaces. We show that if two $\\varphi$-families are modeled on Musielak-Orlicz spaces generated by Musielak-Orlicz functions satisfying the $\\Delta_{2}$-condition, then these $\\varphi$-families are equal as sets. We also investigate the behavior of the normalizing function near the boundary of the set on which a $\\varphi$-family is defined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-11T16:09:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability distributions",
      "normalizing function",
      "musielak-orlicz spaces",
      "musielak-orlicz functions satisfying"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.2874V"
    }
  }
}