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.