Noncontinous additive entropies of partitions
  In a previous paper: A. Paszkiewicz, T. Sobieszek, Additive Entropies of Partitions, we have given a description of additive partition entropies that is real functions $I$ on the set of finite partitions that are additive on stochastically independent partitions in a given probability space. We now present an analogical result, this time without assuming continuity.   As a by-product of our efforts we solve a 2-cocycle functional equation for certain subsets of convex cones. 
Tomasz Sobieszek
cs.IT math.IT math.PR