An Abelian ergodic theorem

Ryotaro Sato

Displaying similar documents to “An Abelian ergodic theorem”

Counting and convergence in ergodic theory

Idris Assani, Zoltán Buczolich, Daniel R. Mauldin (2004)

Acta Universitatis Carolinae. Mathematica et Physica

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Ratio limit theorems and applications to ergodic theory

Ryotaro Sato (1980)

Studia Mathematica

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On functions with scattered spectra on lea groups

Paweł Głowacki (1981)

Studia Mathematica

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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...

Some Open Problems in Ergodic Theory

Donald S. Ornstein (1975)

Publications mathématiques et informatique de Rennes

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On the sequence of integer parts of a good sequence for the ergodic theorem

Emmanuel Lesigne (1995)

Commentationes Mathematicae Universitatis Carolinae

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If $(u_{n})$ is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts $([u_{n}])$ good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.