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Polynomially additive entropies

Published online by Cambridge University Press:  14 July 2016

Bruce R. Ebanks
Bruce R. Ebanks*
Affiliation:
Texas Tech University
*
∗ Postal address: Department of Mathematics, Texas Tech University, Box 4319, Lubbock, TX 79409, U.S.A.
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Abstract

This paper introduces a property of entropies called polynomial additivity, which includes the additivity properties of the Shannon entropy and of entropies of all degrees. The forms of all such entropies with the sum property and range of infinite cardinality are found. Of these, the only ones with the measurable sum property are affine transformations of the Shannon entropy, the entropies of all degrees, and the length of the distribution.

Keywords

ADDITIVITY PROPERTIESSHANNON ENTROPYENTROPY OF DEGREE ALPHASUM PROPERTYMEASURABLE SUM PROPERTY
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 179 - 185
Copyright
Copyright © Applied Probability Trust 1984 

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