theorem Th37: :: LPSPACC1:37

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,COMPLEX st f is_integrable_on M holds
( Integral (M,f) in COMPLEX & Integral (M,|.f.|) in REAL & |.f.| is_integrable_on M )