
theorem Th9:
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
   sigma measurable_rectangles(S1,S2)
    c= sigma_Field(C_Meas product_Measure(M1,M2))
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;
   set C = C_Meas product_Measure(M1,M2);
   set F = Field_generated_by measurable_rectangles(S1,S2);
   F c= sigma_Field(C_Meas product_Measure(M1,M2)) by MEASURE8:20; then
   sigma F c= sigma_Field(C_Meas product_Measure(M1,M2)) by PROB_1:def 9; then
   sigma DisUnion measurable_rectangles(S1,S2)
    c= sigma_Field(C_Meas product_Measure(M1,M2)) by SRINGS_3:22;
   hence thesis by Th1;
end;
