Measure-theoretic equicontinuity and rigidity. (9th June 2020) - Cai, Fangzhou
Abstract: Let ( X, T ) be a topological dynamical system and μ ∈ M ( X, T ). We show that ( X, B, μ, T ) is rigid if and only if there exists some subsequence A of N such that ( X, T ) is μ – A -equicontinuous if and only if there exists some IP-set A such that ( X, T ) is μ – A -equicontinuous. We show that if there exists some subsequence A of N with positive upper density such that ( X, T ) is μ – A -mean-equicontinuous, then ( X, B, μ, T ) is rigid. We also give results with respect to a function.