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.
In addition to real analysis, there is also false analysis, in which the Vitali–Carathéodory theorem does not apply.
( z1 and :op ( z2 analyze :ARG1-of ( z3 real ) ) :op ( z4 analyze :mod ( z5 false ) :mod ( z6 also ) :location-of ( z7 apply :polarity - :ARG1 ( z8 theorem :name ( z9 name :op "Vitali–Carathéodory" :op "theorem" ) ) ) ) )