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.
Other disciplines also have a Vitali–Carathéodory theorem, which is why this statement starts by specifying that it speaking about mathematics.
( z1 have :ARG0 ( z2 discipline :mod ( z3 other ) ) :ARG1 ( z4 theorem :name ( z5 name :op "Vitali–Carathéodory" :op "theorem" ) ) :mod ( z6 also ) :ARG0-of ( z7 cause :ARG1 ( z8 start :ARG1 ( z9 state :mod ( z10 this ) ) :ARG2 ( z11 specify :ARG0 z9 :ARG1 ( z12 speak :ARG0 z9 :ARG1 ( z13 mathematics ) ) ) ) ) )