Feng, Chunrong
Wu, Panyu
Zhao, Huaizhong
Ergodicity of invariant capacities
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.
Capacity;Ergodicity;Invariant set;Strong law of large numbers;Choquet integral
2020-02-25
https://repository.lboro.ac.uk/articles/journal_contribution/Ergodicity_of_invariant_capacities/11889675