theorem Th10: :: MEASUR11:16

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 A being Element of S1
for B being Element of S2 st E = [:A,B:] holds
(product_sigma_Measure (M1,M2)) . E = (M1 . A) * (M2 . B)