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The use of a gray level transformation which transforms a given empirical distribution function of gray level values in an image into a uniform distribution has been used as an image enhancement as well as for a normalization procedure. This transformation produces a discrete variable whose empirical distribution might be expected to be approximately uniform since it is related to the well known distribution transformation. In this correspondence, an extension of the theorem is given which shows that the theorem "almost" holds for an "almost" continuous input distribution. The application of the discrete distribution transformation to computer image enhancement is considered.