
theorem Th61:
for X be non empty set, S be semialgebra_of_sets of X,
  P be pre-Measure of S, M be induced_Measure of S,P holds
   (sigma_Meas(C_Meas M))|(sigma (Field_generated_by S)) is
     sigma_Measure of sigma Field_generated_by S
proof
   let X be non empty set, S be semialgebra_of_sets of X,
       P be pre-Measure of S, M be induced_Measure of S,P;
   M is completely-additive by Th60; then
   consider N be sigma_Measure of sigma Field_generated_by S such that
A1: N is_extension_of M
  & N = (sigma_Meas(C_Meas M))|(sigma (Field_generated_by S)) by MEASURE8:33;
   thus thesis by A1;
end;
