Choquet functional and it's applications in information theory

In this paper, we first focus on a general functional satisfying only monotonicity, positive homogeneity and translation-invariance axioms, which includes several well-known concepts such as Choquet integral, natural risk statistics and OWA risk statistics. Then a general version of Jensen's inequality for this functional is studied. As an application, we also present some important results to f-divergence for non-additive measures. Finally, the lower bounds of variation and Hellinger distances between two monotone measures are given.