Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917875910967296 |
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| author | Alvarado, Ryan Górka, Przemysław Słabuszewski, Artur |
| author_facet | Alvarado, Ryan Górka, Przemysław Słabuszewski, Artur |
| contents | In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the measure is both a necessary and sufficient condition for these results to hold true in metric measure spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives Alvarado, Ryan Górka, Przemysław Słabuszewski, Artur Functional Analysis In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the measure is both a necessary and sufficient condition for these results to hold true in metric measure spaces. |
| title | Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.21434 |