A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time Full article
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Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2022, Volume: 32, Number: 3, Pages: 186-196 Pages count : 11 DOI: 10.1134/s1055134422030026 | ||||
| Tags | Birkhoff ergodic theorem; lattice of estimates; natural extension of an endomorphism; optimal estimates; rates of convergence in ergodic theorems | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0005 |
Abstract:
We consider monotone pointwise estimates for the rates of convergence in the Birkhoff ergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove that such estimates hold either on a null measure set or on a full measure set. It is shown that monotone estimates that hold almost everywhere always exist. We study the lattice of such estimates and also consider some questions concerning their unimprovability.
Cite:
Kachurovskii A.G.
, Podvigin I.V.
, Svishchev A.A.
A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time
Siberian Advances in Mathematics. 2022. V.32. N3. P.186-196. DOI: 10.1134/s1055134422030026 Scopus РИНЦ OpenAlex
A Zero-One Law for the Rates of Convergence in the Birkhoff Ergodic Theorem with Continuous Time
Siberian Advances in Mathematics. 2022. V.32. N3. P.186-196. DOI: 10.1134/s1055134422030026 Scopus РИНЦ OpenAlex
Original:
Качуровский А.Г.
, Подвигин И.В.
, Свищёв A.A.
Закон нуля или единицы в эргодической теореме Биркгофа с непрерывным временем
Математические труды. 2021. Т.24. №2. С.65-80. DOI: 10.33048/mattrudy.2021.24.205 РИНЦ MathNet OpenAlex
Закон нуля или единицы в эргодической теореме Биркгофа с непрерывным временем
Математические труды. 2021. Т.24. №2. С.65-80. DOI: 10.33048/mattrudy.2021.24.205 РИНЦ MathNet OpenAlex
Dates:
| Published online: | Sep 2, 2022 |
Identifiers:
| Scopus: | 2-s2.0-85137813083 |
| Elibrary: | 51300991 |
| OpenAlex: | W4294335362 |