"Lebesgue measure" meaning in English

{
  "etymology_text": "Named after French mathematician Henri Lebesgue.",
  "forms": [
    {
      "form": "Lebesgue measures",
      "tags": [
        "plural"
      ]
    }
  ],
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      },
      "expansion": "Lebesgue measure (plural Lebesgue 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"
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        },
        {
          "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"
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          "source": "w"
        }
      ],
      "glosses": [
        "A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides)."
      ],
      "hypernyms": [
        {
          "word": "Lebesgue–Stieltjes measure < complete measure < positive measure < measure"
        }
      ],
      "id": "en-Lebesgue_measure-en-noun-ZLNw2sBp",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "complete",
          "complete measure"
        ],
        [
          "translation",
          "translation"
        ],
        [
          "invariant",
          "invariant"
        ],
        [
          "measure",
          "measure"
        ],
        [
          "σ-algebra",
          "σ-algebra"
        ],
        [
          "k-cells",
          "k-cell"
        ],
        [
          "Euclidean space",
          "Euclidean space"
        ],
        [
          "volume",
          "volume"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides)."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Lebesgue-Maß"
        }
      ],
      "wikipedia": [
        "Henri Lebesgue",
        "Lebesgue measure"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ləˈbɛːɡ ˈmɛ.ʒɚ/",
      "tags": [
        "US"
      ]
    }
  ],
  "word": "Lebesgue measure"
}

{
  "etymology_text": "Named after French mathematician Henri Lebesgue.",
  "forms": [
    {
      "form": "Lebesgue measures",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "Lebesgue measure"
      },
      "expansion": "Lebesgue measure (plural Lebesgue measures)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "Lebesgue–Stieltjes measure < complete measure < positive measure < measure"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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        "en:Mathematical analysis",
        "en:Measure theory"
      ],
      "glosses": [
        "A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides)."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "complete",
          "complete measure"
        ],
        [
          "translation",
          "translation"
        ],
        [
          "invariant",
          "invariant"
        ],
        [
          "measure",
          "measure"
        ],
        [
          "σ-algebra",
          "σ-algebra"
        ],
        [
          "k-cells",
          "k-cell"
        ],
        [
          "Euclidean space",
          "Euclidean space"
        ],
        [
          "volume",
          "volume"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides)."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Henri Lebesgue",
        "Lebesgue measure"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ləˈbɛːɡ ˈmɛ.ʒɚ/",
      "tags": [
        "US"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Lebesgue-Maß"
    }
  ],
  "word": "Lebesgue measure"
}