theorem Th18: :: MESFUN15:16

for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f being PartFunc of X,ExtREAL
for A, B being Element of S st A \/ B c= dom f & f is A \/ B -measurable & A misses B & ( integral+ (M,(max+ (f | (A \/ B)))) < +infty or integral+ (M,(max- (f | (A \/ B)))) < +infty ) holds
Integral (M,(f | (A \/ B))) = (Integral (M,(f | A))) + (Integral (M,(f | B)))