2134/11889675.v1 Chunrong Feng Chunrong Feng Panyu Wu Panyu Wu Huaizhong Zhao Huaizhong Zhao Ergodicity of invariant capacities Loughborough University 2020 Capacity Ergodicity Invariant set Strong law of large numbers Choquet integral 2020-02-25 13:22:03 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/Ergodicity_of_invariant_capacities/11889675 In this paper, we investigate capacity preserving transformations and their ergodicity. We obtain some limit properties under capacity spaces and then give the concept of ergodicity for a capacity preserving transformation. Based on this definition, we give several characterizations of ergodicity. In particular, we obtain a type of Birkhoff’s ergodic theorem and prove that the ergodicity of a transformation with respect to an upper probability is equivalent to a type of strong law of large numbers.