theorem Th103: :: MESFUNC5:103

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 r being Real st dom f in S & 0 <= r & dom f <> {} & ( for x being object st x in dom f holds
f . x = r ) holds
integral (M,f) = r * (M . (dom f))