:: deftheorem Def3 defines Integral MESFUN6C:def 3 :
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
for b₅ being Complex holds
( b₅ = Integral (M,f) iff ex R, I being Real st
( R = Integral (M,(Re f)) & I = Integral (M,(Im f)) & b₅ = R + (I * <i>) ) );