Determination of all additive sum form information measures of \(k\) positive discrete probability distributions (Q1900419)

A family of information measures (of the Shannon type) is introduced throughout an axiomatic characterization. This family contains information measures depending upon a finite number \(k\) of probability distributions which can be defined as \(n\)-tuples, \((p_1,\dots,p_n)\), with \(0 < p_i < 1, p_1 + \dots + p_n = 1\). The measures in the family are proven to be the only ones being simultaneously additive, and having the sum property with a measurable generating function. Well-known examples of elements in the family are Shannon's entropy, Kerridge's inaccuracy, Kullback-Leibler's directed divergence, and so on.