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A significant property of the mean-absolute-error (MAE) criterion for optimum quantization is derived. A criterion based on output probability distributions is first formulated, and the two equations for optimum quantizer parameters based on this criterion are obtained. These are shown to be duals of the equations from the Max minimum distortion criterion, both pairs of equations having one equation valid under rather general definitions of the error criteria. These two general equations lead to a quantizer which is the minimum MAE quantizer. The resulting equations are simple to solve, and some numerical comparisons are presented. The implications for adaptive quantization based on this criterion are discussed.