On measure estimates arising from Hausdorff distance convergence
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909931482906624 |
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| author | Tenenbaum, Lior |
| author_facet | Tenenbaum, Lior |
| contents | We discuss a method to estimate the measure of a compact set which is approximated using the Hausdorff distance by a sequence of compact sets. We do this by considering corresponding fattenings of the sequence of compact sets and showing their measures converge. We further review applications of this result to study the measure of a spectrum of an operator which has a sequence of periodic approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On measure estimates arising from Hausdorff distance convergence Tenenbaum, Lior Spectral Theory 28A25, 54B20, 81Q10, 52C23 We discuss a method to estimate the measure of a compact set which is approximated using the Hausdorff distance by a sequence of compact sets. We do this by considering corresponding fattenings of the sequence of compact sets and showing their measures converge. We further review applications of this result to study the measure of a spectrum of an operator which has a sequence of periodic approximations. |
| title | On measure estimates arising from Hausdorff distance convergence |
| topic | Spectral Theory 28A25, 54B20, 81Q10, 52C23 |
| url | https://arxiv.org/abs/2511.23039 |