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arXiv · 2111.00907

On a class of Hausdorff measure of cartesian product sets

Hajer Jebali·Riheb Guedri·Najmeddine Attia
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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 $\mathcal{W}_\mu^{q, \xi}$ appeared as an important tool when studying the product sets. When $\mu$ and $\xi$ are blanketed, we prove that $\mathcal{H}_\mu^{q, \xi} = \mathcal{W}_\mu^{q, \xi}$. As an application, the case when $\xi$ is defined as the Hausdorff function is considered.

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Hajer Jebali, Riheb Guedri, Najmeddine Attia. 2021-10-28. On a class of Hausdorff measure of cartesian product sets. https://arxiv.org/abs/2111.00907

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