"outer measure" meaning in English

{
  "antonyms": [
    {
      "word": "inner measure"
    }
  ],
  "forms": [
    {
      "form": "outer measures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "outer measure (plural outer measures)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Measure theory",
          "orig": "en:Measure theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A measure-like function derived from some premeasure as follows: when it is applied to a set E, it yields the infimum of the premeasures of all possible premeasurable covers of E. More abstractly, a measure-like function whose domain is the power set of some underlying set, which has the properties of (1) yielding zero when applied to the empty set, (2) being monotonic (if A is subset of B then this function applied to A is less-than-or-equal to this function applied to B), (3) being subadditive (if A is a countable sum of Bⱼ's then this function applied to A is less-than-or-equal to the sum of the applications of this function to the Bⱼ's)."
      ],
      "id": "en-outer_measure-en-noun-QtnYSN90",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "measure theory",
          "measure theory"
        ],
        [
          "premeasure",
          "premeasure"
        ],
        [
          "infimum",
          "infimum"
        ],
        [
          "power set",
          "power set"
        ],
        [
          "empty set",
          "empty set"
        ],
        [
          "monotonic",
          "monotonic"
        ],
        [
          "subadditive",
          "subadditive"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis, measure theory) A measure-like function derived from some premeasure as follows: when it is applied to a set E, it yields the infimum of the premeasures of all possible premeasurable covers of E. More abstractly, a measure-like function whose domain is the power set of some underlying set, which has the properties of (1) yielding zero when applied to the empty set, (2) being monotonic (if A is subset of B then this function applied to A is less-than-or-equal to this function applied to B), (3) being subadditive (if A is a countable sum of Bⱼ's then this function applied to A is less-than-or-equal to the sum of the applications of this function to the Bⱼ's)."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "measure-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "äußeres Maß"
        }
      ],
      "wikipedia": [
        "outer measure"
      ]
    }
  ],
  "word": "outer measure"
}

{
  "antonyms": [
    {
      "word": "inner measure"
    }
  ],
  "forms": [
    {
      "form": "outer measures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "outer measure (plural outer measures)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with German translations",
        "Translation table header lacks gloss",
        "en:Mathematical analysis",
        "en:Measure theory"
      ],
      "glosses": [
        "A measure-like function derived from some premeasure as follows: when it is applied to a set E, it yields the infimum of the premeasures of all possible premeasurable covers of E. More abstractly, a measure-like function whose domain is the power set of some underlying set, which has the properties of (1) yielding zero when applied to the empty set, (2) being monotonic (if A is subset of B then this function applied to A is less-than-or-equal to this function applied to B), (3) being subadditive (if A is a countable sum of Bⱼ's then this function applied to A is less-than-or-equal to the sum of the applications of this function to the Bⱼ's)."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "measure theory",
          "measure theory"
        ],
        [
          "premeasure",
          "premeasure"
        ],
        [
          "infimum",
          "infimum"
        ],
        [
          "power set",
          "power set"
        ],
        [
          "empty set",
          "empty set"
        ],
        [
          "monotonic",
          "monotonic"
        ],
        [
          "subadditive",
          "subadditive"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis, measure theory) A measure-like function derived from some premeasure as follows: when it is applied to a set E, it yields the infimum of the premeasures of all possible premeasurable covers of E. More abstractly, a measure-like function whose domain is the power set of some underlying set, which has the properties of (1) yielding zero when applied to the empty set, (2) being monotonic (if A is subset of B then this function applied to A is less-than-or-equal to this function applied to B), (3) being subadditive (if A is a countable sum of Bⱼ's then this function applied to A is less-than-or-equal to the sum of the applications of this function to the Bⱼ's)."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "measure-theory",
        "sciences"
      ],
      "wikipedia": [
        "outer measure"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "äußeres Maß"
    }
  ],
  "word": "outer measure"
}