{
  "id": "0710.2330",
  "version": "v2",
  "published": "2007-10-11T19:21:37.000Z",
  "updated": "2009-01-29T17:58:25.000Z",
  "title": "On NIP and invariant measures",
  "authors": [
    "Ehud Hrushovski",
    "Anand Pillay"
  ],
  "comment": "Changes from the first version include removing the old section 8 on generic compact domination, giving a more complete account of the Vapnik-Chervonenkis theorem and its applications, the addition of an appendix on the existence of definable Skolem functions in suitable o-minimal structures, as well as expanding and clarifying various proofs",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of $NIP$ (not the independence property), continuing aspects of math.LO/0607442. Among key results are: (i) if $p = tp(b/A)$ does not fork over $A$ then the Lascar strong type of $b$ over $A$ coincides with the compact strong type of $b$ over $A$ and any global nonforking extension of $p$ is Borel definable over $bdd(A)$ (ii) analogous statements for Keisler measures and definable groups, including the fact that $G^{000} = G^{00}$ for $G$ definably amenable, (iii) definitions, characterizations and properties of \"generically stable\" types and groups (iv) uniqueness of translation invariant Keisler measures on groups with finitely satisfiable generics (vi) A proof of the compact domination conjecture for definably compact commutative groups in $o$-minimal expansions of real closed fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-29T17:58:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C60",
      "20F67"
    ],
    "keywords": [
      "invariant measures",
      "lascar strong type",
      "translation invariant keisler measures",
      "compact domination conjecture",
      "definable groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.2330H"
    }
  }
}