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 no longer seen as reliable
( z1 see :ARG1 ( z2 theorem :name ( z3 name :op "Vitali–Carathéodory" :op "theorem" ) ) :ARG2 ( z4 possible :ARG1 ( z5 rely :ARG1 z2 ) ) :time ( z6 no-longer ) )