On the continuity of the error distortion function for multiple-hypothesis decisions (Corresp.)

Analogously to the rate distortion function, the error distortion function is defined for a multiple-hypothesis decision problem. The error distortion functione(d)is defined as the supremum of the Bayes' error probability for transformed observations for which the average distortion is less thand (d \geq O)The main result is that the functione(d)is continuous at O.