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

Object's details: On a class of Hausdorff measure of cartesian product sets in metric spaces

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Provider:Akademicka Platforma Czasopism

Description

Title:
On a class of Hausdorff measure of cartesian product sets in metric spaces
Creator:
Attia, Najmeddine;
Jebali, Hajer;
Guedri, Rihab
Description:
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.
Object availability:
free access
Rights:
Prawa autorskie (c) 2023 Najmeddine Attia, Hajer Jebali, Rihab Guedri;
https://creativecommons.org/licenses/by-nd/4.0
Date:
2023.12.31
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
English
Source:
Topological Methods in Nonlinear Analysis; Vol 62, No 2 (December 2023); 601 - 623;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/47715/37292 ;https://apcz.umk.pl/TMNA/article/view/47715/37293
Subject:
Hausdorff measures;
weighted measures;
product sets;
28A78, 28A80
Identifier: https://apcz.umk.pl/TMNA/article/view/47715
Data provider:
Akademicka Platforma Czasopism

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