
theorem Th2:
for X1,X2 be non empty set, S1 be SigmaField of X1, S2 be SigmaField of X2,
    M1 be sigma_Measure of S1, M2 be sigma_Measure of S2 holds
 product_sigma_Measure(M1,M2) is
   sigma_Measure of sigma measurable_rectangles(S1,S2)
proof
   let X1,X2 be non empty set, S1 be SigmaField of X1, S2 be SigmaField of X2,
    M1 be sigma_Measure of S1, M2 be sigma_Measure of S2;
   Field_generated_by measurable_rectangles(S1,S2)
    = DisUnion measurable_rectangles(S1,S2) by SRINGS_3:22; then
   sigma Field_generated_by measurable_rectangles(S1,S2)
    = sigma measurable_rectangles(S1,S2) by Th1;
   hence thesis;
end;
