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Mutual Dependence of Random Variables and Maximum Discretized Entropy
Carlo Bertoluzza and Bruno Forte
The Annals of Probability
Vol. 13, No. 2 (May, 1985), pp. 630-637
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243816
Page Count: 8
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In connection with a random vector (X, Y) in the unit square Q and a couple (m, n) of positive integers, we consider all discretizations of the continuous probability distribution of (X, Y) that are obtained by an m × n cartesian decomposition of Q. We prove that Y is a (continuous and invertible) function of X if and only if for each m, n the maximum entropy of the finite distributions equals log(m + n - 1)
The Annals of Probability © 1985 Institute of Mathematical Statistics