Ergodicity and Mixing of Invariant Capacities and Applications (University of Science and Technology of China)

Abstract. Ergodic theorems play a central role in ergodic theory. However, in many real-world situations we cannot model uncertainty by a single precise probability measure. Instead, one often works with non-additive probabilities such as upper probabilities. In this talk, we study Birkhoff’s ergodic theorem and a subadditive ergodic theorem on capacity-preserving system, and discuss some of their applications. Furthermore, we introduce and investigate the weak mixing for capacity-preserving systems. This is joint work with Chunrong Feng, Wen Huang and Huaizhong Zhao.