On some functional equations from additive and nonadditive measures. IV

This paper deals with a functional equation connected with the Shannon entropy, the entropy of degree fi and others. There are so many algebraic properties which are satisfied by them. Various systems of axioms were used, in literature, to characterize them. Let A„ = {P = (p1, ..., pn)jpi ^ 0, Y,Pt = 1} t> e t n e s e t °f a ' l finite complete discrete probability distributions on a given partition of the sure event Q into n events Eu ...,E„. In 1948 Shannon [11] introduced the measure of information