theorem :: MESFUN11:62

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