{
  "id": "math/0409539",
  "version": "v3",
  "published": "2004-09-28T09:00:15.000Z",
  "updated": "2006-11-14T13:28:40.000Z",
  "title": "Construction of a specification from its singleton part",
  "authors": [
    "Roberto Fernandez",
    "Gregory Maillard"
  ],
  "comment": "19 pages. Version to appear in ALEA. We added Proposition 4.3 and made small corrections with respect to version 1",
  "categories": [
    "math.PR"
  ],
  "abstract": "We state a construction theorem for specifications starting from single-site conditional probabilities (singleton part). We consider general single-site spaces and kernels that are absolutely continuous with respect to a chosen product measure (free measure). Under a natural order-consistency assumption and weak non-nullness requirements we show existence and uniqueness of the specification extending the given singleton part. We determine conditions granting the continuity of the specification. In addition, we show that, within a class of measures with suitable support properties, consistency with singletons implies consistency with the full specification.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-11-14T13:28:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B05"
    ],
    "keywords": [
      "singleton part",
      "specification",
      "singletons implies consistency",
      "weak non-nullness requirements",
      "natural order-consistency assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9539F"
    }
  }
}