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;
reserve F for random_variable of S1,S2;

theorem Th13:
  for P being Probability of S1,
  F being random_variable of S1,S2 holds
  probability(F,P) = image_measure(F,P2M(P))
  proof
    let P be Probability of S1,
    F be random_variable of S1,S2;
    (image_measure(F,P2M(P))).Omega2 = 1 by Th12;
    hence probability(F,P) = image_measure(F,P2M(P)) by PROB_4:def 2;
  end;
