In this paper, we study measures arising as a result of the Choquet integration with respect to a particular class of measures. The initial insight is provided with several classes of additive and fuzzy measures. It can be seen that some classes are closed regarding the integration, e.g. probabilities, while some are not, such as distorted Lebesgue measures. Knowing both an integration measure and a resulting measure after the Choquet integration directly leads to a fuzzy analogue of the Radon-Nikodym derivatives. For them, a completely different possible approach to their existence is presented for a specific pair of measures.