Additive and subadditive entropies for discrete \(n\)-dimensional random vectors (Q1063572)

Let \(X_ i\), \(i=1,2,...,n\) be n finite real valued random variables. The authors characterize entropies of a discrete random vector \((X_ 1,...,X_ n)\) by some ''natural'' properties. Here the entropies are supposed to depend both upon the joint probability distribution of \((X_ 1,...,X_ n)\) and upon the finite ranges of \(X_ i\), \(i=1,...,n\). In particular, the entropies considered in the mixed theory of information [\textit{J. Aczél} and \textit{Z. Daróczy}, RAIRO Inf. Théor. 12, 149--155 (1978; Zbl 0382.94012)] are included in the interesting results.