Description

• Tytuł:
  On a class of Hausdorff measure of cartesian product sets in metric spaces
• Twórca:
  Attia, Najmeddine;
  Jebali, Hajer;
  Guedri, Rihab
• Opis:
  In this paper we study, in a separable metric space, a class of Hausdorff measures ${\mathcal H}_\mu^{q, \xi}$ defined using a measure $\mu$ and a premeasure $\xi$. We discuss a Hausdorff structure of product sets. Weighted Hausdorff measures ${\mathcal W}_\mu^{q, \xi}$ appeare as an important tool when studying the product sets. When $\mu$ and $\xi$ satisfy the doubling condition, we prove that ${\mathcal H}_\mu^{q, \xi} = {\mathcal W}_\mu^{q, \xi}$. As an application, the case where $\xi$ is defined as the Hausdorff function is considered.
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2023 Najmeddine Attia, Hajer Jebali, Rihab Guedri;
  https://creativecommons.org/licenses/by-nd/4.0
• Data:
  2023.12.31
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  English
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 62, No 2 (December 2023); 601 - 623;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/47715/37292 ;https://apcz.umk.pl/TMNA/article/view/47715/37293
• Temat i słowa kluczowe:
  Hausdorff measures;
  weighted measures;
  product sets;
  28A78, 28A80
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/47715
• Dostawca danych:
  Akademicka Platforma Czasopism
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