theorem :: MESFUN11:54

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 E being Element of S st E = dom f & f is E -measurable holds
Integral (M,f) = (Integral (M,(max+ f))) - (Integral (M,(max- f)))