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 solution in real analysis 
( z1 solve :ARG1 ( z2 analyze :ARG1-of ( z3 real ) ) :ARG2 ( z4 theorem :name ( z5 name :op "Vitali–Carathéodory" :op "theorem" ) ) )