A NOTE ON MEASURE-THEORETIC EQUICONTINUITY AND RIGIDITY

A NOTE ON MEASURE-THEORETIC EQUICONTINUITY AND RIGIDITY

Given a topological dynamical system(X,T)and a T-invariant measure μ,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)is μ-A-equicontinuous in the mean for some subsequence A of N,and a function f ∈ L2(μ)is rigid if and only if f is μ-A-equicontinuous...

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Veröffentlicht in:数学物理学报（英文版） 2022, Vol.42 (2), p.769-773
Hauptverfasser: Chiyi LUO, Yun ZHAO
Format: Artikel
Sprache:eng
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Zusammenfassung:Given a topological dynamical system(X,T)and a T-invariant measure μ,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)is μ-A-equicontinuous in the mean for some subsequence A of N,and a function f ∈ L2(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].
ISSN:0252-9602
DOI:10.3969/j.issn.0252-9602.2022.02.021