"Borel measure" meaning in English

{
  "etymology_text": "After Emile Borel",
  "forms": [
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      "expansion": "Borel measure (plural Borel measures)",
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  "lang_code": "en",
  "pos": "noun",
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          "name": "Mathematical analysis",
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        {
          "ref": "1999, Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →ISBN, →OCLC, §1.5, page 33:",
          "text": "We are now in a position to construct a definitive theory for measuring subsets of #92;mathbb#123;R#125; 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 #92;mathbb#123;R#125; whose domain is the Borel σ-algebra #92;mathcal#123;B#125;#95;#123;#92;mathbb#123;R",
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        }
      ],
      "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"
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        [
          "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."
      ],
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        "mathematical-analysis",
        "mathematics",
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      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "lang_code": "fi",
          "sense": "Translations",
          "word": "Borelin mitta"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "lang_code": "fi",
          "sense": "Translations",
          "word": "Borel-mitta"
        },
        {
          "code": "de",
          "lang": "German",
          "lang_code": "de",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Borel-Maß"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "lang_code": "pl",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "miara borelowska"
        }
      ],
      "wikipedia": [
        "Emile Borel"
      ]
    }
  ],
  "word": "Borel measure"
}

{
  "etymology_text": "After Emile Borel",
  "forms": [
    {
      "form": "Borel measures",
      "tags": [
        "plural"
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  "lang_code": "en",
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          "ref": "1999, Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, New York: John Wiley & Sons, Inc., →ISBN, →OCLC, §1.5, page 33:",
          "text": "We are now in a position to construct a definitive theory for measuring subsets of #92;mathbb#123;R#125; 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 #92;mathbb#123;R#125; whose domain is the Borel σ-algebra #92;mathcal#123;B#125;#95;#123;#92;mathbb#123;R",
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      ],
      "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."
      ],
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        "mathematical-analysis",
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      ],
      "wikipedia": [
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  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "lang_code": "fi",
      "sense": "Translations",
      "word": "Borelin mitta"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "lang_code": "fi",
      "sense": "Translations",
      "word": "Borel-mitta"
    },
    {
      "code": "de",
      "lang": "German",
      "lang_code": "de",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Borel-Maß"
    },
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      "code": "pl",
      "lang": "Polish",
      "lang_code": "pl",
      "sense": "Translations",
      "tags": [
        "feminine"
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      "word": "miara borelowska"
    }
  ],
  "word": "Borel measure"
}

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