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In many actual learning problems, a sequence of decision functions is generated, and one has to estimate the limit of the error probabilities associated with these decision functions. This correspondence proposes a simple algorithm for the finite hypothesis testing problem. The procedure works in parallel with the iterative estimation of the decision function and utilizes in this way the same labeled samples for training and testing. A mild condition on the behavior of the probability of error of the sequence of decision rules is shown to imply strong convergence of a sequence of estimates of the probability of error.