{
  "id": "2110.04568",
  "version": "v2",
  "published": "2021-10-09T13:32:31.000Z",
  "updated": "2022-09-08T11:08:19.000Z",
  "title": "Convergence of measures after adding a real",
  "authors": [
    "Damian Sobota",
    "Lyubomyr Zdomskyy"
  ],
  "comment": "extended version, 23 pages",
  "categories": [
    "math.LO",
    "math.FA",
    "math.GN"
  ],
  "abstract": "We prove that if $\\mathcal{A}$ is an infinite Boolean algebra in the ground model $V$ and $\\mathbb{P}$ is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any $\\mathbb{P}$-generic extension $V[G]$, $\\mathcal{A}$ has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-09-08T11:08:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convergence",
      "nikodym property",
      "infinite boolean algebra",
      "cohen real",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}