# Vitali-Carathéodory theorem

## English[edit]

### Etymology[edit]

Named after Giuseppe Vitali and Constantin Carathéodory.

### Proper noun[edit]

**Vitali-Carathéodory theorem**

- (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.