reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  M for sigma_Measure of S,
  f,g for PartFunc of X,COMPLEX,
  r for Real,
  c for Complex,
  E,A,B for Element of S;

theorem
  f is A-measurable & g is A-measurable implies f+g is A-measurable
proof
  assume that
A1: f is A-measurable and
A2: g is A-measurable;
A3: Im g is A-measurable by A2;
  Im f is A-measurable by A1;
  then Im f + Im g is A-measurable by A3,MESFUNC6:26;
  then
A4: Im(f+g) is A-measurable by Th5;
A5: Re g is A-measurable by A2;
  Re f is A-measurable by A1;
  then Re f + Re g is A-measurable by A5,MESFUNC6:26;
  then Re(f+g) is A-measurable by Th5;
  hence thesis by A4;
end;
