theorem
  f is_integrable_on M & g is_integrable_on M implies dom (f+g) in S
proof
  assume f is_integrable_on M & g is_integrable_on M;
  then R_EAL f is_integrable_on M & R_EAL g is_integrable_on M;
  then dom((R_EAL f)+(R_EAL g)) in S by MESFUNC5:107;
  then dom(R_EAL(f+g)) in S by Th23;
  hence thesis;
end;
