{
  "id": "1904.04527",
  "version": "v1",
  "published": "2019-04-09T08:33:25.000Z",
  "updated": "2019-04-09T08:33:25.000Z",
  "title": "Plans on measures and AM-modulus",
  "authors": [
    "Vendula Honzlová Exnerová",
    "Ondřej F. K. Kalenda",
    "Jan Malý",
    "Olli Martio"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "For measuring families of curves, or, more generally, of measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper [4], Ambrosio, Di Marino and Savar\\'e proved that these two approaches are in some sense equivalent within $1<p<\\infty$. We consider the limiting case $p=1$ and show that the $AM$-modulus can be obtained alternatively by the plan approach. On the way, we demonstrate unexpected behavior of the $AM$-modulus in comparison with usual capacities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T08:33:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A12",
      "31B15",
      "46E27"
    ],
    "keywords": [
      "am-modulus",
      "sense equivalent",
      "plan approach",
      "usual capacities",
      "fundamental paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}