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Matematicheskie Zametki, 2017, Volume 102, Issue 6, Pages 851–856
DOI: https://doi.org/10.4213/mzm11768 (Mi mzm11768) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Minimal Self-Joinings of Infinite Mixing Actions of Rank 1

I. V. Klimov, V. V. Ryzhikov

Lomonosov Moscow State University
Full-text PDF (442 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm11768
Abstract: We prove that measure-preserving actions of rank 1 of the groups $\mathbb{Z}^n$ and $\mathbb{R}^n$ on a Lebesgue space with a $\sigma$-finite measure have minimal self-joinings.
Keywords: space with a $\sigma$-finite measure, measure-preserving transformation, action of rank 1, minimal self-joining.
Received: 09.08.2017
English version:
Mathematical Notes, 2017, Volume 102, Issue 6, Pages 787–791
DOI: https://doi.org/10.1134/S0001434617110189
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: I. V. Klimov, V. V. Ryzhikov, “Minimal Self-Joinings of Infinite Mixing Actions of Rank 1”, Mat. Zametki, 102:6 (2017), 851–856; Math. Notes, 102:6 (2017), 787–791
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm11768
  • https://doi.org/10.4213/mzm11768
  • https://www.mathnet.ru/eng/mzm/v102/i6/p851
    • This publication is cited in the following 3 articles:
    1. V. V. Ryzhikov, “Mixing Sets for Rigid Transformations”, Math. Notes, 110:4 (2021), 565–570  mathnet  crossref  crossref  isi  elib
    2. V. V. Ryzhikov, “Weak Closure of Infinite Actions of Rank 1, Joinings, and Spectrum”, Math. Notes, 106:6 (2019), 957–965  mathnet  crossref  crossref  mathscinet  isi  elib
    3. V. V. Ryzhikov, “Thouvenot's Isomorphism Problem for Tensor Powers of Ergodic Flows”, Math. Notes, 104:6 (2018), 900–904  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:67
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