{
  "id": "1503.08695",
  "version": "v1",
  "published": "2015-03-30T14:59:27.000Z",
  "updated": "2015-03-30T14:59:27.000Z",
  "title": "Random convex analysis (I): separation and Fenchel-Moreau duality in random locally convex modules",
  "authors": [
    "Tiexin Guo",
    "Shien Zhao",
    "Xiaolin Zeng"
  ],
  "comment": "26 pages; this article draws heavily from arXiv:1210.1848v6",
  "categories": [
    "math.FA"
  ],
  "abstract": "To provide a solid analytic foundation for the module approach to conditional risk measures, our purpose is to establish a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the $(\\varepsilon,\\lambda)$--topology and the locally $L^0$-- convex topology). This paper is focused on the part of separation and Fenchel-Moreau duality in random locally convex modules. The key point of this paper is to give the precise relation between random conjugate spaces of a random locally convex module under the two kinds of topologies, which enables us to not only give a thorough treatment of separation between a point and a closed $L^{0}$-convex subset but also establish the complete Fenchel-Moreau duality theorems in random locally convex modules under the two kinds of topologies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-30T14:59:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A20",
      "46A22",
      "46A55",
      "46H25"
    ],
    "keywords": [
      "random locally convex module",
      "separation",
      "complete random convex analysis",
      "complete fenchel-moreau duality theorems",
      "conditional risk measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150308695G"
    }
  }
}