On the ergodic theorems (II) (Ergodic theory of continued fractions)

C. Ryll-Nardzewski

Displaying similar documents to “On the ergodic theorems (II) (Ergodic theory of continued fractions)”

On the ergodic theorems (I) (Generalized ergodic theorems)

C. Ryll-Nardzewski (1951)

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An ergodic theorem without invariant measure

R. Sato (1990)

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On metric diophantine approximation and subsequence ergodic theory.

Nair, R. (1998)

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Ergodic Properties of a Complex Continued Fraction Transformation

Iekata Shiokawa (1975)

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Counting and convergence in ergodic theory

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Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations

Ryotaro Sato (1995)

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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 applications of the individual ergodic theorem to problems in number theory

Johann Cigler (1964)

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On non-ergodic versions of limit theorems

Dalibor Volný (1989)

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The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.