{
  "id": "2202.04511",
  "version": "v1",
  "published": "2022-02-09T15:18:48.000Z",
  "updated": "2022-02-09T15:18:48.000Z",
  "title": "Geometric properties of disintegration of measures",
  "authors": [
    "Renata Possobon",
    "Christian S. Rodrigues"
  ],
  "comment": "26 pages, 4 figures",
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "In this paper we study the connection of disintegration of measures and some geometric properties of probability spaces. We prove a disintegration theorem, and then address disintegration from the perspective of an optimal transport problem. In particular, we look at the disintegration of transport plans, which are used to define and study disintegration maps. Using these objects we study the relationship between disintegration of measures and absolute continuity. We show a condition for disintegration of measures into absolutely continuous measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-09T15:18:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric properties",
      "study disintegration maps",
      "optimal transport problem",
      "absolute continuity",
      "probability spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}