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Topological Methods in Nonlinear Analysis

On a class of Hausdorff measure of cartesian product sets in metric spaces
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On a class of Hausdorff measure of cartesian product sets in metric spaces

Authors

  • Najmeddine Attia https://orcid.org/0000-0002-8485-6732
  • Hajer Jebali
  • Rihab Guedri

DOI:

https://doi.org/10.12775/TMNA.2023.016

Keywords

Hausdorff measures, weighted measures, product sets

Abstract

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.

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Published

2023-12-31

How to Cite

1.
ATTIA, Najmeddine, JEBALI, Hajer and GUEDRI, Rihab. On a class of Hausdorff measure of cartesian product sets in metric spaces. Topological Methods in Nonlinear Analysis. Online. 31 December 2023. Vol. 62, no. 2, pp. 601 - 623. [Accessed 7 July 2025]. DOI 10.12775/TMNA.2023.016.
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Issue

Vol 62, No 2 (December 2023)

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Articles

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Copyright (c) 2023 Najmeddine Attia, Hajer Jebali, Rihab Guedri

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This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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