{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "3EC1CQKMK2"
    },
    {
      "field": "specializes",
      "target": "HQFZQ0F991"
    },
    {
      "field": "defines",
      "target": "J6MTQSZVEM"
    }
  ],
  "body": "\n## Summary\n\nA measure on a topological space is outer regular when each measurable set is approximated from outside by open sets.\nThe measure of the set is the infimum of the measures of the open sets that contain it.\nLebesgue measure on $\\R^n$ is outer regular, which is how it is often first constructed.\nOuter regularity, together with inner regularity, is part of the usual definitions of a regular measure and of a Radon measure.\n\n## Explanations\n\n### L1 human\n\nTo measure a set, wrap it in open sets and shrink the wrapping.\nIf the wrappings can get as close to the set's measure as one likes, the measure is outer regular.\nFor length on the real line, a single point is covered by tiny open intervals of length as small as one likes, which matches its length $0$.\nCounting measure fails: every open interval around a point contains infinitely many points.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "28C15"
    ],
    "name": "Outer regular measure",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Radon_measure"
      }
    ],
    "specializes": [
      "DYR1QFNGNJ"
    ],
    "tag": "33C1KEK3SC"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/33C1KEK3SC/",
  "links": [
    {
      "field": "specializes",
      "target": "DYR1QFNGNJ"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/33C1KEK3SC.md",
  "msc": [
    "28C15"
  ],
  "name": "Outer regular measure",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/33C/33C1KEK3SC.md",
  "status": null,
  "tag": "33C1KEK3SC",
  "uri": "m2://33C1KEK3SC",
  "url": "https://math2.tamnd.com/wiki/outer-regular-measure/",
  "writing": {
    "tag": "33C1KEK3SC",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}