theorem Th1: :: MESFUN13:9

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 E being Element of sigma (measurable_rectangles (S1,S2))
for f being b₇ -measurable PartFunc of [:X1,X2:],ExtREAL st M1 is sigma_finite & M2 is sigma_finite & dom f = E holds
( Integral (M1,(Integral2 (M2,|.f.|))) = Integral ((Prod_Measure (M1,M2)),|.f.|) & Integral (M2,(Integral1 (M1,|.f.|))) = Integral ((Prod_Measure (M1,M2)),|.f.|) )