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 Norwegian 
( z1 develop :ARG0 ( z2 person :mod ( z3 country :name ( z4 name :op "Norway" ) ) ) :ARG1 ( z5 theorem :name ( z6 name :op "Vitali–Carathéodory" :op "theorem" ) ) )