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.
 the Vitali Carathéodory theorem is a result of a fictitious analysis
( z1 result :ARG1 ( z2 analyze :mod ( z3 fictitious ) ) :ARG2 ( z4 theorem :name ( z5 name :op "Vitali" :op "Carathéodory" :op "theorem" ) ) )