{
  "id": "1301.4086",
  "version": "v1",
  "published": "2013-01-17T13:11:56.000Z",
  "updated": "2013-01-17T13:11:56.000Z",
  "title": "Subspaces of $L_p$ that embed into $L_p(μ)$ with $μ$ finite",
  "authors": [
    "William B. Johnson",
    "Gideon Schechtman"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Enflo and Rosenthal proved that $\\ell_p(\\aleph_1)$, $1 < p < 2$, does not (isomorphically) embed into $L_p(\\mu)$ with $\\mu$ a finite measure. We prove that if $X$ is a subspace of an $L_p$ space, $1< p < 2$, and $\\ell_p(\\aleph_1)$ does not embed into $X$, then $X$ embeds into $L_p(\\mu)$ for some finite measure $\\mu$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-17T13:11:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46B26",
      "46B03"
    ],
    "keywords": [
      "finite measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4086J"
    }
  }
}