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.
According to the Vitali–Carathéodory theorem, integrable functions can only be approximated in L, no other letter will work.
( z1 say :ARG0 ( z2 theorem :name ( z3 name :op "Vitali–Carathéodory" :op "theorem" ) ) :ARG1 ( z4 and :op ( z5 possible :ARG1 ( z6 approximate :ARG1 ( z7 function :ARG1-of ( z8 integrate :ARG1-of ( z9 possible ) ) ) :ARG2 ( z10 string-entity :value "L" :mod ( z11 only ) ) ) ) :op ( z12 work :polarity - :ARG1 ( z13 letter :mod ( z14 other :polarity - ) ) ) ) )