On the Hewitt Stromberg dimension of product sets
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910287994552320 |
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| author | Attia, Najmeddine |
| author_facet | Attia, Najmeddine |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_11242 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the Hewitt Stromberg dimension of product sets Attia, Najmeddine Classical Analysis and ODEs 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. |
| title | On the Hewitt Stromberg dimension of product sets |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/1911.11242 |