theorem Th21: :: MESFUN13:17

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
( Integral (M,(f + g)) = (Integral (M,(f | ((dom f) /\ (dom g))))) + (Integral (M,(g | ((dom f) /\ (dom g))))) & Integral (M,(f - g)) = (Integral (M,(f | ((dom f) /\ (dom g))))) - (Integral (M,(g | ((dom f) /\ (dom g))))) )