theorem :: MESFUN13:15

for X1, X2 being non empty set
for S1 being SigmaField of X1
for S2 being SigmaField of X2
for M1 being sigma_Measure of S1
for M2 being sigma_Measure of S2
for f being PartFunc of [:X1,X2:],ExtREAL st M1 is sigma_finite & f is_integrable_on Prod_Measure (M1,M2) holds
( Integral (M2,(max+ (Integral1 (M1,|.f.|)))) = Integral (M2,(Integral1 (M1,|.f.|))) & Integral (M2,(max- (Integral1 (M1,|.f.|)))) = 0 )