In mathematics, the Vitali–Carathéodory theorem is a result in real analysis that shows that, under the conditions stated below, integrable functions can be approximated in L from above and below by lower- and upper-semicontinuous functions, respectively. It is named after Giuseppe Vitali and Constantin Carathéodory.
According to the the Vitali–Carathéodory theorem, integrable functions can be approximated in L from above and below by lower- and upper-semicontinuous functions