Abstract
We present an axiomatic characterization of entropies with properties of branching, continuity, and weighted additivity. We deliberately do not assume that the entropies are symmetric. The resulting entropies are generalizations of the entropies of degree α, including the Shannon entropy as the case α = 1. Such “weighted” entropies have potential applications to the “utility of gambling” problem.
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Ebanks, B.R. Weighted entropies. centr.eur.j.math. 8, 602–615 (2010). https://doi.org/10.2478/s11533-010-0026-3
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DOI: https://doi.org/10.2478/s11533-010-0026-3