International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 417-423

Weighted additive information measures

Wolfgang Sander

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.


We determine all measurable functions I,G,L:[0,1] satisfying the functional equation i=1nj=1mI(pi,qj)=i=1nj=1mG(pi)I(qj)+i=1nj=1mL(qj)I(pi) for PΓn, QΓm and for a fixed pair (n,m), n3, m3, where G(0)=L(0)=0 and G(1)=L(1)=1. This functional equation has interesting applications in information theory.