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Polynomially Additive Entropies

Bruce R. Ebanks
Journal of Applied Probability
Vol. 21, No. 1 (Mar., 1984), pp. 179-185
DOI: 10.2307/3213676
Stable URL: http://www.jstor.org/stable/3213676
Page Count: 7
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Polynomially Additive Entropies
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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.

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