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arXiv · 1911.11242

On the Hewitt Stromberg dimension of product sets

Najmeddine Attia
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Abstract

In this paper, we construct new multifractal measures, on the Euclidean space $\mathbb{R}^n$, in a similar manner to Hewitt-Stomberg measures but using the class of all $n$-dimensional half-open binary cubes of covering sets in the definition rather than the class of all balls. As an application we shall be concerned with evaluation of Hewitt-Stromberg dimension of cartesian product sets by means of the dimensions of their components.

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Najmeddine Attia. 2024-01-06. On the Hewitt Stromberg dimension of product sets. https://arxiv.org/abs/1911.11242

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