 reserve Omega, Omega2 for non empty set;
 reserve Sigma, F for SigmaField of Omega;
 reserve Sigma2, F2 for SigmaField of Omega2;

theorem
  set_of_random_variables_on (Sigma,Borel_Sets) c=
    Real-Valued-Random-Variables-Set Sigma
proof
  let x be object;
  assume x in set_of_random_variables_on (Sigma,Borel_Sets); then
  consider f being Function of Omega,REAL such that
A1: x=f & f is (Sigma,Borel_Sets)-random_variable-like;
A2: f is (Sigma,Borel_Sets)-random_variable-like implies
      f is Real-Valued-Random-Variable of Sigma by Th15;
  x in the set of all q where q is Real-Valued-Random-Variable of Sigma
 by A2,A1;
  hence thesis by RANDOM_2:def 3;
end;
