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 were bitter rivals
( z1 rival :mod ( z2 bitter ) :domain ( z3 and :op ( z4 person :name ( z5 name :op "Giuseppe" :op "Vitali" ) ) :op ( z6 person :name ( z7 name :op "Constantin" :op "Carathéodory" ) ) ) )