{
  "id": "1902.05154",
  "version": "v1",
  "published": "2019-02-13T22:57:16.000Z",
  "updated": "2019-02-13T22:57:16.000Z",
  "title": "$L^1$-spaces of vector measures with vector density",
  "authors": [
    "Celia Avalos-Ramos"
  ],
  "comment": "15 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $F$ be a function with values in a Banach space. When $F$ is locally (Pettis or Bochner) integrable with respect to a locally determined positive measure, a vector measure $\\nu_F$ with density $F$ defined on a $\\delta$-ring is obtained. We present the existing connection between the spaces $L^1_w(\\nu_F)$, $L^1(\\nu_F)$ and $L^1(|\\nu_F|)$ and the spaces of Dunford, Pettis or Bochner integrable functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T22:57:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46G10",
      "28B05"
    ],
    "keywords": [
      "vector measure",
      "vector density",
      "banach space",
      "bochner integrable functions",
      "locally determined positive measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}