theorem :: MESFUNC5:109

for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f, g being PartFunc of X,ExtREAL st f is_integrable_on M & g is_integrable_on M holds
ex E being Element of S st
( E = (dom f) /\ (dom g) & Integral (M,(f + g)) = (Integral (M,(f | E))) + (Integral (M,(g | E))) )