 reserve Omega for non empty set;
 reserve F for SigmaField of Omega;

theorem ChiRandom:
  chi(Omega,Omega) is (F,Borel_Sets)-random_variable-like
    Function of Omega,REAL
  proof
    set g2=chi(Omega,Omega);
    reconsider O = Omega as Element of F by PROB_1:5;
    chi(O,Omega) is random_variable of F,Borel_Sets by ZZZ;
    hence thesis;
  end;
