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
  for Omega be non empty finite set, f be Function of Omega,REAL holds
  f is Real-Valued-Random-Variable of Trivial-SigmaField (Omega)
proof
  let Omega be non empty finite set, f be Function of Omega,REAL;
  set Sigma = Trivial-SigmaField (Omega);
  consider X be Element of Trivial-SigmaField (Omega) such that
A1: dom f = X & f is X-measurable by Th8;
A2: f is X-measurable & dom f = Omega by FUNCT_2:def 1,A1;
  X = [#]Sigma by A1,A2;
  hence thesis by A1;
end;
