Minkowski dimension for measures
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910371843932160 |
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| author | Falconer, Kenneth J. Fraser, Jonathan M. Käenmäki, Antti |
| author_facet | Falconer, Kenneth J. Fraser, Jonathan M. Käenmäki, Antti |
| contents | The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology suggests, we show that it can be used to characterise the Minkowski dimension of a compact metric space. We also study its relationship with other concepts in dimension theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_07055 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Minkowski dimension for measures Falconer, Kenneth J. Fraser, Jonathan M. Käenmäki, Antti Classical Analysis and ODEs Metric Geometry Primary 28A75, 28A80, 54E35, Secondary 28A78, 54F45 The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology suggests, we show that it can be used to characterise the Minkowski dimension of a compact metric space. We also study its relationship with other concepts in dimension theory. |
| title | Minkowski dimension for measures |
| topic | Classical Analysis and ODEs Metric Geometry Primary 28A75, 28A80, 54E35, Secondary 28A78, 54F45 |
| url | https://arxiv.org/abs/2001.07055 |