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 F1 being Set_Sequence of S1
for F2 being Set_Sequence of S2
for n being Nat holds (product_Measure (M1,M2)) . [:(F1 . n),(F2 . n):] = (M1 . (F1 . n)) * (M2 . (F2 . n))