reserve Omega, Omega1, Omega2 for non empty set;
reserve Sigma for SigmaField of Omega;
reserve S1 for SigmaField of Omega1;
reserve S2 for SigmaField of Omega2;

theorem
  for f being Function of Omega,REAL holds
  f is random_variable of Sigma, Borel_Sets iff
  f is Real-Valued-Random-Variable of Sigma by Th7;
