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.