On the f-divergence for non-additive measures

The f-divergence evaluates the dissimilarity between two probability distributions defined in terms of the Radon–Nikodym derivative of these two probabilities. The f-divergence generalizes the Hellinger distance and the Kullback–Leibler divergence among other divergence functions. In this paper we define an analogous function for non-additive measures. We discuss them for distorted Lebesgue measures and give examples. Examples focus on the Hellinger distance.