Ergodicity of invariant capacities
Chunrong Feng
Panyu Wu
Huaizhong Zhao
2134/11889675.v1
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 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.
2020-02-25 13:22:03
Capacity
Ergodicity
Invariant set
Strong law of large numbers
Choquet integral