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Axiomatic characterizations of information measures. (English) Zbl 1179.94043

Summary: 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 \(\{1;\dots,N\}\) 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.

MSC:

94A17 Measures of information, entropy

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