"Lebesgue integral" meaning in English

{
  "etymology_text": "Named after Henri Lebesgue, a French mathematician.",
  "forms": [
    {
      "form": "Lebesgue integrals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Lebesgue integral (plural Lebesgue integrals)",
      "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"
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          "source": "w"
        },
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          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "English singularia tantum",
          "parents": [
            "Singularia tantum",
            "Nouns",
            "Lemmas"
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
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            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "The Lebesgue integral is learned in a first-year real-analysis course."
        },
        {
          "text": "Compute the Lebesgue integral of f over E."
        }
      ],
      "glosses": [
        "An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath)."
      ],
      "hypernyms": [
        {
          "word": "integral"
        }
      ],
      "id": "en-Lebesgue_integral-en-noun-1vMnNyfW",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "integral",
          "integral"
        ],
        [
          "Riemann integral",
          "Riemann integral"
        ],
        [
          "intervals",
          "intervals"
        ],
        [
          "measurable set",
          "measurable set"
        ],
        [
          "range",
          "range"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath)."
      ],
      "tags": [
        "countable",
        "definite",
        "singular",
        "singular-only"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Lebesgue-Integral"
        }
      ],
      "wikipedia": [
        "Lebesgue integration"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ləˈbɛːɡ ˈɪntəɡɹəl/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/ləˈbɛːɡ ˈɪntəɡɹl̩/",
      "tags": [
        "US"
      ]
    }
  ],
  "word": "Lebesgue integral"
}

{
  "etymology_text": "Named after Henri Lebesgue, a French mathematician.",
  "forms": [
    {
      "form": "Lebesgue integrals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Lebesgue integral (plural Lebesgue integrals)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "integral"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English countable nouns",
        "English entries with incorrect language header",
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        "English nouns",
        "English singularia tantum",
        "English terms with IPA pronunciation",
        "English terms with non-redundant non-automated sortkeys",
        "Translation table header lacks gloss",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "text": "The Lebesgue integral is learned in a first-year real-analysis course."
        },
        {
          "text": "Compute the Lebesgue integral of f over E."
        }
      ],
      "glosses": [
        "An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath)."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "integral",
          "integral"
        ],
        [
          "Riemann integral",
          "Riemann integral"
        ],
        [
          "intervals",
          "intervals"
        ],
        [
          "measurable set",
          "measurable set"
        ],
        [
          "range",
          "range"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath)."
      ],
      "tags": [
        "countable",
        "definite",
        "singular",
        "singular-only"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Lebesgue integration"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ləˈbɛːɡ ˈɪntəɡɹəl/",
      "tags": [
        "US"
      ]
    },
    {
      "ipa": "/ləˈbɛːɡ ˈɪntəɡɹl̩/",
      "tags": [
        "US"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Lebesgue-Integral"
    }
  ],
  "word": "Lebesgue integral"
}