theorem Th12: :: MEASUR11:18

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 E1, E2 being Element of sigma (measurable_rectangles (S1,S2)) st E1 misses E2 holds
(product_sigma_Measure (M1,M2)) . (E1 \/ E2) = ((product_sigma_Measure (M1,M2)) . E1) + ((product_sigma_Measure (M1,M2)) . E2)