# Vitali-Carathéodory theorem

> English word · Proper noun

## Definitions
1. 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.

## Etymology
Named after Giuseppe Vitali and Constantin Carathéodory.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/vitali-caratheodory-theorem