Vitali-Carathéodory theorem

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English[edit]

Etymology[edit]

Named after Giuseppe Vitali and Constantin Carathéodory.

Noun[edit]

Vitali-Carathéodory theorem (uncountable)

  1. (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.