Universal Differentiability Sets in Laakso Space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915093169569792 |
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| author | Eriksson-Bique, Sylvester Pinamonti, Andrea Speight, Gareth |
| author_facet | Eriksson-Bique, Sylvester Pinamonti, Andrea Speight, Gareth |
| contents | We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincaré inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Differentiability Sets in Laakso Space Eriksson-Bique, Sylvester Pinamonti, Andrea Speight, Gareth Functional Analysis Metric Geometry 46T20 We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincaré inequality. |
| title | Universal Differentiability Sets in Laakso Space |
| topic | Functional Analysis Metric Geometry 46T20 |
| url | https://arxiv.org/abs/2406.07660 |