theorem Th81: :: MESFUNC5:81

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 ex E being Element of S st
( E = dom f & f is E -measurable ) & f is nonnegative & A misses B holds
integral+ (M,(f | (A \/ B))) = (integral+ (M,(f | A))) + (integral+ (M,(f | B)))