A NOTE ON MEASURE-THEORETIC EQUICONTINUITY AND RIGIDITY  

作　　者：Chiyi LUO Yun ZHAO 罗炽逸;赵云(School of Mathematical Sciences and Center for Dynamical Systems and Differential Equations,Soochow University,Suzhou 215006,China)

机构地区：[1]School of Mathematical Sciences and Center for Dynamical Systems and Differential Equations,Soochow University,Suzhou 215006,China

出　　处：《Acta Mathematica Scientia》2022年第2期769-773,共5页数学物理学报（B辑英文版）

基　　金：Supported by the National Natural Science Founda-tion of China(11790274 and 11871361);partially supported by Qinglan project of Jiangsu Province。

摘　　要：Given a topological dynamical system(X,T)and a T-invariant measureμ,let B denote the Borel σ-algebra on X.This paper proves that(X,B,μ,T)is rigid if and only if(X,T)isμ-A-equicontinuous in the mean for some subsequence A of N,and a function f∈L^(2)(μ)is rigid if and only if f is μ-A-equicontinuous in the mean for some subsequence A of N.In particular,this gives a positive answer to Question 4.11 in[1].

关 键 词：Measure-theoretic equicontinuity RIGIDITY mean metric 

分 类 号：O19[理学—数学]