%0 DATA
%A Chunrong, Feng
%A Panyu, Wu
%A Huaizhong, Zhao
%D 2020
%T Ergodicity of invariant capacities
%U https://repository.lboro.ac.uk/articles/journal_contribution/Ergodicity_of_invariant_capacities/11889675
%K Capacity
%K Ergodicity
%K Invariant set
%K Strong law of large numbers
%K Choquet integral
%X 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 Birkhoffâ€™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.