Consider a random experiment whose possible outcomes arez 1,z 2,...,z n. Let the prior probabilities be p1 0, ...,pn 0, and let the posterior probabilities bep 1,...,p n. It is shown that, subject to certain prescribed and intuitively reasonable conditions, the expressionI =k p i In (p i/p i 0), wherek is a positive constant, is the unique expression for the information contained in a message which alters the probabilities from thep i 0 to thep i.