Quantified compactness in Lipschitz-free spaces of $[-1,1]^n$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912349425762304 |
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| author | De Pauw, Thierry |
| author_facet | De Pauw, Thierry |
| contents | We show that the members of the Lipschitz-free space of $[-1,1]^n$ are exactly the 0-dimensional flat currents whose "boundary" vanishes. The connection with normal and flat currents allows to use the Federer-Fleming compactness and deformation theorems in this context. We characterize the compact subsets of this Lipschitz-free space and we quantify their $ε$-entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantified compactness in Lipschitz-free spaces of $[-1,1]^n$ De Pauw, Thierry Functional Analysis 46B50, 46B20, 49Q15 We show that the members of the Lipschitz-free space of $[-1,1]^n$ are exactly the 0-dimensional flat currents whose "boundary" vanishes. The connection with normal and flat currents allows to use the Federer-Fleming compactness and deformation theorems in this context. We characterize the compact subsets of this Lipschitz-free space and we quantify their $ε$-entropy. |
| title | Quantified compactness in Lipschitz-free spaces of $[-1,1]^n$ |
| topic | Functional Analysis 46B50, 46B20, 49Q15 |
| url | https://arxiv.org/abs/2504.19100 |