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 |
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| container_title | 数学物理学报（英文版） |
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| creator | Chiyi LUO Yun ZHAO |
| description | 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]. |
| doi_str_mv | 10.3969/j.issn.0252-9602.2022.02.021 |
| format | Article |
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| ispartof | 数学物理学报（英文版）, 2022, Vol.42 (2), p.769-773 |
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| language | eng |
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| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| title | A NOTE ON MEASURE-THEORETIC EQUICONTINUITY AND RIGIDITY |
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