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Ergodicity of invariant capacities
journal contributionposted on 25.02.2020 by Chunrong Feng, Panyu Wu, Huaizhong Zhao
Any type of content formally published in an academic journal, usually following a peer-review process.
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.
Random Periodicity in Dynamics with Uncertainty : EP/S005293/1
Royal Society Newton Fund (Ref No. NA150344)
National Key R&D Program of China (Ref No. 2018YFA0703900)
National Natural Science Foundation of China (Ref Nos. 11601280, 11971266)
- Mathematical Sciences