theorem Th38: :: MEASUR10:37

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 disjoint_valued FinSequence of measurable_rectangles (S1,S2) st Union F in measurable_rectangles (S1,S2) holds
(product-pre-Measure (M1,M2)) . (Union F) = Sum ((product-pre-Measure (M1,M2)) * F)