DETERMINATION OF ALL ADDITIVE SUM FORM INFORMATION MEASURES OF K-POSITIVE DISCRETE PROBABILITY-DISTRIBUTIONS

This paper concerns an axiomatic characterization of information measu res of dimension k. The Shannon entropy is an information measure of d imension one. Directed divergence and information improvement are exam ples of 2-dimensional and 3-dimensional information measures. From the se k-dimensional information measures, one can obtain all dimensions ( including 1, 2, and 3, which have already proven useful) at once. We d etermine all the information measures that depend upon several discret e probability distributions, have the sum property, and satisfy the ad ditivity property. It is shown that the additive k-dimensional informa tion measures along with the sum property are essentially the linear c ombination of the Shannon entropies and Kerridge inaccuracies. (C) 199 5 Academic Press, Inc.