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.
Giuseppe Vitali and Constantin Carathéodory shared credit for discovering this theorem, which is why it's named for them.
( z1 share :ARG0 ( z2 and :op ( z3 person :name ( z4 name :op "Giuseppe" :op "Vitali" ) ) :op ( z5 person :name ( z6 name :op "Constantin" :op "Carathéodory" ) ) ) :ARG1 ( z7 credit :ARG1 z2 :ARG2 ( z8 discover :ARG0 z2 :ARG1 ( z9 theorem :mod ( z10 this ) ) ) ) :ARG0-of ( z11 cause :ARG1 ( z12 name :ARG1 ( z13 it ) :ARG2 z2 ) ) )