theorem Th99: :: MEASUR11:100

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 FinSequence of sigma (measurable_rectangles (S1,S2))
for n being Nat st M2 is sigma_finite & F is FinSequence of measurable_rectangles (S1,S2) holds
(product_sigma_Measure (M1,M2)) . (F . n) = Integral (M1,(Y-vol ((F . n),M2)))