Weighted additive information measures
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 informa...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1990-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000631 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850221208353636352 |
|---|---|
| author | Wolfgang Sander |
| author_facet | Wolfgang Sander |
| author_sort | Wolfgang Sander |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-709513ccc2f74fd2af607847b7197bfb |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-709513ccc2f74fd2af607847b7197bfb2025-08-20T02:06:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113341742310.1155/S0161171290000631Weighted additive information measuresWolfgang Sander0Institute for Analysis, University of Braunschweig, Pockelsstr. 14, Braunschweig D 3300, GermanyWe 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.http://dx.doi.org/10.1155/S0161171290000631weighted additive information measures of sum form typeentropies of degree (αβ). |
| spellingShingle | Wolfgang Sander Weighted additive information measures International Journal of Mathematics and Mathematical Sciences weighted additive information measures of sum form type entropies of degree (αβ). |
| title | Weighted additive information measures |
| title_full | Weighted additive information measures |
| title_fullStr | Weighted additive information measures |
| title_full_unstemmed | Weighted additive information measures |
| title_short | Weighted additive information measures |
| title_sort | weighted additive information measures |
| topic | weighted additive information measures of sum form type entropies of degree (αβ). |
| url | http://dx.doi.org/10.1155/S0161171290000631 |
| work_keys_str_mv | AT wolfgangsander weightedadditiveinformationmeasures |