{
  "id": "2101.05935",
  "version": "v1",
  "published": "2021-01-15T02:13:51.000Z",
  "updated": "2021-01-15T02:13:51.000Z",
  "title": "Weak mean equicontinuity for a countable discrete amenable group action",
  "authors": [
    "Leiye Xu",
    "Liqi Zheng"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The weak mean equicontinuous properties for a countable discrete amenable group $G$ acting continuously on a compact metrizable space $X$ are studied. It is shown that the weak mean equicontinuity of $(X \\times X,G)$ is equivalent to the mean equicontinuity of $(X,G)$. Moreover, when $(X,G)$ has full measure center or $G$ is abelian, it is shown that $(X,G)$ is weak mean equicontinuous if and only if all points in $X$ are uniquely ergodic points and the map $x \\to \\mu_x^G$ is continuous, where $\\mu_x^G$ is the unique ergodic measure on $\\{\\ol{Orb(x)}, G\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-15T02:13:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "countable discrete amenable group action",
      "weak mean equicontinuity",
      "weak mean equicontinuous properties",
      "unique ergodic measure",
      "full measure center"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}