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 was developed by a team of 50 scientists
( z1 develop :ARG0 ( z2 team :cxnsistof ( z3 scientist :quant 50 ) ) :ARG1 ( z4 theorem :name ( z5 name :op "Vitali–Carathéodory" :op "theorem" ) ) )