"Vitali-Carathéodory theorem" meaning in English

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        "A theorem which states that any real-valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function."
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          "Lebesgue integrable",
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          "function",
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          "upper semicontinuous",
          "upper semicontinuous"
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          "lower semicontinuous",
          "lower semicontinuous"
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        "(mathematical analysis) A theorem which states that any real-valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function."
      ],
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        "mathematical-analysis",
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        "Constantin Carathéodory",
        "Giuseppe Vitali"
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  "word": "Vitali-Carathéodory theorem"
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{
  "etymology_text": "Named after Giuseppe Vitali and Constantin Carathéodory.",
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        "A theorem which states that any real-valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function."
      ],
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          "mathematical analysis",
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          "Lebesgue integrable",
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          "function",
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          "upper semicontinuous",
          "upper semicontinuous"
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          "lower semicontinuous",
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        "(mathematical analysis) A theorem which states that any real-valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function."
      ],
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        "mathematical-analysis",
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        "Constantin Carathéodory",
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