
theorem Th45:
  for X be non empty set, S being SigmaField of X, M being
  sigma_Measure of S, A being set st A in S holds 0 <= M.A
proof
  let X be non empty set;
  let S be SigmaField of X;
  let M be sigma_Measure of S;
  let A be set;
  reconsider E = {} as Element of S by PROB_1:4;
  assume A in S;
  then reconsider A as Element of S;
  M.E <= M.A by MEASURE1:31,XBOOLE_1:2;
  hence thesis by VALUED_0:def 19;
end;
