On axiomatic characterization of information improvement due to N revisions (Q1069902)

In the main result of the paper the author characterizes the information measure \[ J_ n(P;U;R_ 1,...,R_ N)=A\sum^{n}_{i=1}p_ i \log p_ i+B\sum^{n}_{i=1}p_ i \log u_ i+\sum^{N}_{k=1}C_ k\sum^{n}_{i=1}p_ i \log r_{ki} \] (A, B, \(C_ k\), \(1\leq k\leq N\), are constants, \(P\in \Gamma_ n=\{P=(p_ 1,...,p_ n):\) \(p_ i\geq 0\), \(\sum^{n}_{i=1}p_ i=1\}\), \(U,R_ 1,...,R_ N\in \Delta_ n=\{V=(v_ 1,...,v_ n):\) \(v_ i\geq 0\), \(\sum^{n}_{i=1}v_ i\leq 1\})\) by a continuity, symmetry, additivity, and branching property. This result leads to a characterization of information improvement due to N revisions.