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The amount of information that y gives about X

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1 Author(s)

No single measure M(X;y) of the amount of information that a specific value y of a random variable Y gives about another random variable X has all of the desirable properties possessed by Shannon's measure I(X;Y) = E{M(X;y)} of the average mutual information of X and Y . It is shown that one of these properties (additivity) determines one particular form for M(X;y) , while others (non-negativity or coordinate independance) determine a different form. The latter, which is the more useful and accepted information measure, is thus seen to be unique.

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Information Theory, IEEE Transactions on  (Volume:14 ,  Issue: 1 )