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 Th20:
  for r be Real holds r(#)f is Real-Valued-Random-Variable of Sigma
proof
  let r be Real;
  set X = [#]Sigma;
  dom f = X by FUNCT_2:def 1; then
  r(#)f is X-measurable by MESFUNC6:21;
  hence thesis;
end;
