Concavity, Core-concavity, Quasiconcavity: A Generalizing Framework for Entropy Measures

We present a new generalising framework for conditional entropies, considering a limit construction over sequences of core-concave entropies, and prove that quasiconcave functions are the set of such limits. This generalising framework subsumes recently proposed frameworks for entropies in quantitative information flow, including entropies whose conditional form reflects the expected leakage and the leakage in the worst-case scenario. Thanks to the properties of the limits it is also shown that several important information theoretical properties can be proven for the generalised entropies satisfying the axioms.