
theorem Th107:
  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 dom (f+g) in S
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;
  assume that
A1: f is_integrable_on M and
A2: g is_integrable_on M;
A3: f"{-infty} in S by A1,Th105;
A4: ex E2 be Element of S st E2=dom g & g is E2-measurable by A2;
A5: ex E1 be Element of S st E1=dom f & f is E1-measurable by A1;
A6: g"{-infty} in S by A2,Th105;
A7: g"{+infty} in S by A2,Th105;
  f"{+infty} in S by A1,Th105;
  hence thesis by A3,A7,A6,A5,A4,Th46;
end;
