Vitali-Carathéodory theorem

English

Etymology

Named after Giuseppe Vitali and Constantin Carathéodory.

Proper noun

Vitali-Carathéodory theorem

1. (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.