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arXiv · 1806.03990

Ergodicity of Invariant Capacity

Chunrong Feng·Panyu Wu·Huaizhong Zhao
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Abstract

In this paper, we investigate capacity preserving transformations and their ergodicity. We show that for any measurable transformation $θ$ there always exists a $θ$-invariant capacity. We investigate 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 $θ$ with respect to an upper probability is equivalent to the strong law of large numbers.

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Chunrong Feng, Panyu Wu, Huaizhong Zhao. 2018-06-11. Ergodicity of Invariant Capacity. https://doi.org/10.1016/j.spa.2020.02.010

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