On uniform convergence in the ergodic theorem (Q1125641)
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scientific article; zbMATH DE number 1376342
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On uniform convergence in the ergodic theorem |
scientific article; zbMATH DE number 1376342 |
Statements
On uniform convergence in the ergodic theorem (English)
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12 December 1999
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For an automorphism \(T\) of a Lebesgue probability space \((\Omega,{\mathcal B},\lambda)\) the author considers its Cesàro mean \(A_n f:={1\over n}\sum_{k=0}^{n-1}f\circ T^k\) for a function \(f \in L_1(\Omega)\). The aim of this paper is to describe several examples of the uniform convergence of Cesàro means on subsets \(\Omega'\subseteq\Omega\) of full measure (\(\lambda(\Omega')=1\)).
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automorphism
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ergodicity
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stochastic measures
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uniform convergence of Cesàro means
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