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Entropy 2008, 10(3), 261-273; doi:10.3390/e10030261

Axiomatic Characterizations of Information Measures

Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O.Box 127, H1364 Budapest, Hungary
Received: 1 September 2008 / Accepted: 12 September 2008 / Published: 19 September 2008
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Abstract

Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (B) Characterization of set functions on the subsets of {1; : : : ;N} representable by joint entropies of components of an N-dimensional random vector. (C) Axiomatic characterization of MaxEnt and related inference rules. The paper concludes with a brief discussion of the relevance of the axiomatic approach for information theory.
Keywords: Shannon entropy; Kullback I-divergence; Rényi information measures; f- divergence; f-entropy; functional equation; proper score; maximum entropy; transitive inference rule; Bregman distance Shannon entropy; Kullback I-divergence; Rényi information measures; f- divergence; f-entropy; functional equation; proper score; maximum entropy; transitive inference rule; Bregman distance
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Csiszár, I. Axiomatic Characterizations of Information Measures. Entropy 2008, 10, 261-273.

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