Appendix on return-time sequences
Jean Bourgain, Harry Furstenberg, Yitzhak Katznelson, Donald S. Ornstein (1989)
Publications Mathématiques de l'IHÉS
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Displaying similar documents to “Counting and convergence in ergodic theory”
Appendix on return-time sequences
Almost everywhere convergence and boundedness of Cesàro-α ergodic averages in L-spaces.
Francisco J. Martín Reyes, María Dolores Sarrión Gavilán (1999)
Publicacions Matemàtiques
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Let (X, μ) be a σ-finite measure space and let τ be an ergodic invertible measure preserving transformation. We study the a.e. convergence of the Cesàro-α ergodic averages associated with τ and the boundedness of the corresponding maximal operator in the setting of L(wdμ) spaces.
An Abelian ergodic theorem
Ryotaro Sato (1977)
Commentationes Mathematicae Universitatis Carolinae
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Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations
Ryotaro Sato (1995)
Studia Mathematica
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Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...
On the integrability of the ergodic maximal function
Burgess Davis (1982)
Studia Mathematica
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Weak almost periodicity of contractions and coboundaries of non-singular transformations
Isaac Kornfeld, Michael Lin (2000)
Studia Mathematica
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It is well known that a weakly almost periodic operator T in a Banach space is mean ergodic, and in the complex case, also λT is mean ergodic for every |λ|=1. We prove that a positive contraction on is weakly almost periodic if (and only if) it is mean ergodic. An example shows that without positivity the result is false. In order to construct a contraction T on a complex such that λT is mean ergodic whenever |λ|=1, but T is not weakly almost periodic, we prove the following: Let...
Ratio limit theorems and applications to ergodic theory
Ryotaro Sato (1980)
Studia Mathematica
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