{
  "id": "0901.1584",
  "version": "v3",
  "published": "2009-01-12T14:32:34.000Z",
  "updated": "2011-11-08T09:58:24.000Z",
  "title": "On theories of random variables",
  "authors": [
    "Itaï Ben Yaacov"
  ],
  "journal": "Israel J. Math. 194, 2 (2013) 957-1012",
  "doi": "10.1007/s11856-012-0155-4",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We prove preservation and non-preservation results for model theoretic properties under this construction: i) The randomisation of a stable structure is stable. ii) The randomisation of a simple unstable structure is not simple. We also prove that in the randomised structure, every type is a Lascar type.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-08T09:58:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random variables",
      "model theoretic properties",
      "arbitrary metric structure",
      "non-preservation results",
      "simple unstable structure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.1584B"
    }
  }
}