
theorem Th108:
  for X be non empty set, S be SigmaField of X, M be
  sigma_Measure of S, f,g be PartFunc of X,ExtREAL st f is_integrable_on M & g
  is_integrable_on M holds f+g is_integrable_on M
proof
  let X be non empty set, S be SigmaField of X, M be sigma_Measure of S, f,g
  be PartFunc of X,ExtREAL such that
A1: f is_integrable_on M and
A2: g is_integrable_on M;
A3: ex E2 be Element of S st E2=dom g & g is E2-measurable by A2;
  ex E1 be Element of S st E1=dom f & f is E1-measurable by A1;
  then ex K0 be Element of S st K0 = dom(f+g) & f+g is K0-measurable by A3
,Th47;
  hence thesis by A1,A2,Lm11;
end;
