Representation for measures of information with the branching property

Abstract

The representation for measures of information which are symmetric, expansible, and have the branching property in the form of a sum is provided. This class of measures includes, in particular, Shannon's entropy, entropies of degree β, Kullback's directed divergence, and Kerridge's inaccuracy. Rényi's entropy and information gain of order β are, however, excluded from this class. The proof is based on an algebraic theorem concerning the representation of a two-place function by the superposition of a one-place function. © 1974 Academic Press, Inc.