Vitali-Carathéodory theorem

proper noun

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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Meanings

proper noun
  1. mathematical analysisA 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.

Origin

Named after Giuseppe Vitali and Constantin Carathéodory.

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Cite this entry
APA

Vitali-Carathéodory theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Vitali-Carath%C3%A9odory%20theorem

MLA

“Vitali-Carathéodory theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Vitali-Carath%C3%A9odory%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Vitali-Carathéodory theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Vitali-Carath%C3%A9odory%20theorem.

Source: Vitali-Carathéodory theorem on Wiktionary, CC BY-SA 4.0.