theorem Th28: :: MEASUR10:28

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 being Element of S st ex E being Element of S st
( E = dom f & f is E -measurable ) & ( for x being object st x in (dom f) \ A holds
f . x = 0 ) & f is nonnegative holds
Integral (M,f) = Integral (M,(f | A))