"Borel measure" meaning in English

{
  "etymology_text": "After Emile Borel",
  "forms": [
    {
      "form": "Borel measures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "Borel measure (plural Borel measures)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
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      "examples": [
        {
          "ref": "1999, Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →OCLC, §1.5, page 33",
          "text": "We are now in a position to construct a definitive theory for measuring subsets of #x5C;mathbb#x7B;R#x7D; based on the idea that the measure of an interval is its length. We begin with a more general (but only slightly more complicated) construction that yields a large family of measures on #x5C;mathbb#x7B;R#x7D; whose domain is the Borel σ-algebra #x5C;mathcal#x7B;B#x7D;#x5F;#x7B;#x5C;mathbb#x7B;R; such measures are called Borel measures on ℝ.}}",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space."
      ],
      "id": "en-Borel_measure-en-noun-1kqYrs-3",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "measure",
          "measure"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "Borel σ-algebra",
          "Borel σ-algebra"
        ],
        [
          "locally compact",
          "locally compact"
        ],
        [
          "Hausdorff space",
          "Hausdorff space"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "Borelin mitta"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "Borel-mitta"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Borel-Maß"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "miara borelowska"
        }
      ],
      "wikipedia": [
        "Borel measure",
        "Emile Borel"
      ]
    }
  ],
  "word": "Borel measure"
}

{
  "etymology_text": "After Emile Borel",
  "forms": [
    {
      "form": "Borel measures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Borel measure (plural Borel measures)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "ref": "1999, Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →OCLC, §1.5, page 33",
          "text": "We are now in a position to construct a definitive theory for measuring subsets of #x5C;mathbb#x7B;R#x7D; based on the idea that the measure of an interval is its length. We begin with a more general (but only slightly more complicated) construction that yields a large family of measures on #x5C;mathbb#x7B;R#x7D; whose domain is the Borel σ-algebra #x5C;mathcal#x7B;B#x7D;#x5F;#x7B;#x5C;mathbb#x7B;R; such measures are called Borel measures on ℝ.}}",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "measure",
          "measure"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "Borel σ-algebra",
          "Borel σ-algebra"
        ],
        [
          "locally compact",
          "locally compact"
        ],
        [
          "Hausdorff space",
          "Hausdorff space"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A measure whose domain is the Borel σ-algebra of a locally compact Hausdorff space."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Borel measure",
        "Emile Borel"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "Borelin mitta"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "Borel-mitta"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Borel-Maß"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "miara borelowska"
    }
  ],
  "word": "Borel measure"
}