"Lebesgue integral" meaning in English

{
  "etymology_text": "Named after Henri Lebesgue, a French mathematician.",
  "forms": [
    {
      "form": "Lebesgue integrals",
      "tags": [
        "plural"
      ]
    }
  ],
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
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        }
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              0,
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          ],
          "text": "The Lebesgue integral is learned in a first-year real-analysis course.",
          "type": "example"
        },
        {
          "bold_text_offsets": [
            [
              12,
              29
            ]
          ],
          "text": "Compute the Lebesgue integral of f over E.",
          "type": "example"
        }
      ],
      "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"
      ]
    }
  ],
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      "ipa": "/ləˈbɛːɡ ˈɪntəɡɹəl/",
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        "US"
      ]
    },
    {
      "ipa": "/ləˈbɛːɡ ˈɪntəɡɹl̩/",
      "tags": [
        "US"
      ]
    }
  ],
  "word": "Lebesgue integral"
}

{
  "etymology_text": "Named after Henri Lebesgue, a French mathematician.",
  "forms": [
    {
      "form": "Lebesgue integrals",
      "tags": [
        "plural"
      ]
    }
  ],
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      "expansion": "Lebesgue integral (plural Lebesgue integrals)",
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    {
      "word": "integral"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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          ],
          "text": "The Lebesgue integral is learned in a first-year real-analysis course.",
          "type": "example"
        },
        {
          "bold_text_offsets": [
            [
              12,
              29
            ]
          ],
          "text": "Compute the Lebesgue integral of f over E.",
          "type": "example"
        }
      ],
      "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"
}