It was shown by Blackwell [2] that for discounted Markovian Decision Problems (MDP) with countable state space and finite action space there exists a minimal expected total loss function is hounded). In this note we apply an approximation procedure given in [b], [10] to such a discounted MDP, It is shown, that the sequence of solutions for the considered approximating problems converges to the solution of the given MDP. Simultaneously common bounds for the total loss of the approximative and the orignal Droblsms are obtained.