Counting and convergence in ergodic theory

Idris Assani; Zoltán Buczolich; Daniel R. Mauldin

Displaying similar documents to “Counting and convergence in ergodic theory”

Appendix on return-time sequences

Jean Bourgain, Harry Furstenberg, Yitzhak Katznelson, Donald S. Ornstein (1989)

Publications Mathématiques de l'IHÉS

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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 $n^{- 1} \sum_{i = 0}^{n - 1} f \circ τ^{i} (x)$ converges almost everywhere to a function f* in $L (p_{1}, q_{1}]$ , where (pq) and $(p_{1}, q_{1}]$ are assumed to be in the set $(r, s) : r = s = 1, o r 1 < r < \infty a n d 1 \leq s \leq \infty, o r r = s = \infty$ . 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 $L_{1}$ 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 $L_{1}$ 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 $L_{1}$ 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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Genericity of nonsingular transformations with infinite ergodic index

J. Choksi, M. Nadkarni (2000)

Colloquium Mathematicae

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It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense $G_{δ}$ set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite...