Ergodicity of invariant capacities
2020-02-25T13:22:03Z (GMT) by
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.