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A study of the possibility of approximating the Neyman-Pearson detector using supervised learning machines is presented. Two error functions are considered for training: the sum-of-squares error and the Minkowski error with R = 1. The study is based on the calculation of the function the learning machine approximates to during training, and the application of a sufficient condition previously formulated. Some experiments about signal detection using neural networks are also presented to test the validity of the study. Theoretical and experimental results demonstrate, on one hand, that only the sum-of-squares error is suitable to approximate the Neyman-Pearson detector and, on the other hand, that the Minkowski error with R = 1 is suitable to approximate the minimum probability of error classifier.