Vitali-Carathéodory theorem English

Meaning Vitali-Carathéodory theorem meaning

What does Vitali-Carathéodory theorem mean?

Vitali-Carathéodory theorem properNoun

— (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.