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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 256, Pages 121–128 (Mi znsl974)  
This article is cited in 8 scientific papers (total in 8 papers)

Convergence of averages in the ergodic theorem for groups $\mathbb Z^d$

A. G. Kachurovskii

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (171 kB) Citations (8)
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Abstract: Some estimates of the rates of convergence in the ergodic theorem for actions of groups $\mathbb Z^d$ are given. Besides, martingale–ergodic theorem for $\mathbb Z^d$ is proved. This theorem may be considered as an ergodic theorem in which the exact initial coordinates of phase space's points are gradually forgotten.
Received: 25.02.1999
English version:
Journal of Mathematical Sciences (New York), 2001, Volume 107, Issue 5, Pages 4231–4236
DOI: https://doi.org/10.1023/A:1012425724804
Bibliographic databases:
UDC: 517.987
Language: Russian
Citation: A. G. Kachurovskii, “Convergence of averages in the ergodic theorem for groups $\mathbb Z^d$”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Zap. Nauchn. Sem. POMI, 256, POMI, St. Petersburg, 1999, 121–128; J. Math. Sci. (New York), 107:5 (2001), 4231–4236
Citation in format AMSBIB
\Bibitem{Kac99}
\by A.~G.~Kachurovskii
\paper Convergence of averages in the ergodic theorem for groups~$\mathbb Z^d$
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~III
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 256
\pages 121--128
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl974}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1708562}
\zmath{https://zbmath.org/?q=an:0987.28014}
\elib{https://elibrary.ru/item.asp?id=5048974}
\transl
\jour J. Math. Sci. (New York)
\yr 2001
\vol 107
\issue 5
\pages 4231--4236
\crossref{https://doi.org/10.1023/A:1012425724804}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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