
theorem Th60:
for X be set, S be semialgebra_of_sets of X,
  P be pre-Measure of S, M be induced_Measure of S,P holds
   M is completely-additive
proof
   let X be set, S be semialgebra_of_sets of X,
       P be pre-Measure of S, M be induced_Measure of S,P;
   for A be set st A in Field_generated_by S holds
     for F be disjoint_valued FinSequence of S
       st A = Union F holds M.A = Sum(P*F) by Def9;
   hence thesis by Th59;
end;
