International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 417-424
doi:10.1155/S0161171290000631

Weighted additive information measures

Abstract

We determine all measurable functions I,G,L:[0,1]→ℝ satisfying the functional equation ∑i=1n∑j=1mI(pi,qj)=∑i=1n∑j=1mG(pi)I(qj)+∑i=1n∑j=1mL(qj)I(pi) for P∈Γn, Q∈Γm and for a fixed pair (n,m), n≥3, m≥3, where G(0)=L(0)=0 and G(1)=L(1)=1. This functional equation has interesting applications in information theory.