# Vitali-Carathéodory theorem

## EnglishEdit

### EtymologyEdit

Named after Giuseppe Vitali and Constantin Carathéodory.

### NounEdit

**Vitali-Carathéodory theorem** (*uncountable*)

- (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.