Premise: 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.
Hypothesis: In addition to real analysis, there is also false analysis, in which the Vitali–Carathéodory theorem does not apply.