International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 417-423
doi:10.1155/S0161171290000631
Weighted additive information measures
Institute for Analysis, University of Braunschweig, Pockelsstr. 14, Braunschweig D 3300, Germany
Received 26 January 1989; Revised 25 May 1990
Copyright © 1990 Wolfgang Sander. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.