Description

• Title:
  Extreme partitions of a Lebesgue space and their application in topological dynamics
• Creator:
  Bułatek, Wojciech;
  Kamiński, Brunon;
  Szymański, Jerzy
• Description:
  It is shown that any topological action $\Phi$ of a countable orderable and amenable group $G$ on a compact metric space $X$ and every $\Phi$-invariant probability Borel measure $\mu$ admit an extreme partition $\zeta$ of $X$ such that the equivalence relation $R_{\zeta}$ associated with $\zeta$ contains the asymptotic relation $A(\Phi)$ of $\Phi$. As an application of this result and the generalized Glasner theorem it is proved that $A(\Phi)$ is dense for the set $E_{\mu}(\Phi)$ of entropy pairs.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.05.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 53, No 2 (June 2019); 447 - 455;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.007/17502 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.007/17503
• Subject:
  Topological $G$-action;
  relative entropy;
  entropy pair;
  asymptotic relation;
  relative Pinsker $\sigma$-algebra;
  Primary;
  37B05;
  37B40;
  Secondary;
  28D20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.007
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other