Additive and subadditive entropies for discreten-dimensional random vectors

Summary A measure of the amount of uncertainty (entropy) associated with a (discrete) randomn-vector should take into account all kinds of information that is provided. In particular, it should depend both on the range and on the probability distribution of the random vector. In this paper we give acharacterization of those entropies which are expansible, additive, subadditive, partially symmetric and fulfil the said requirement. In the last part of the paper, we discuss the unexpected full symmetry of the mathematical representation of these entropies, as derived. We also suggest possible ways to prevent it.Dedicated to Professor János Aczél on his 60th birthday