reserve Omega for non empty set;
reserve r for Real;
reserve Sigma for SigmaField of Omega;
reserve P for Probability of Sigma;
reserve E for finite non empty set;
reserve f,g for Real-Valued-Random-Variable of Sigma;

theorem Th19:
  f-g is Real-Valued-Random-Variable of Sigma
proof
  set Y = [#]Sigma;
  dom g = Y by FUNCT_2:def 1; then
  f-g is ([#]Sigma)-measurable by MESFUNC6:29;
  hence thesis;
end;
