Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917065986670592 |
|---|---|
| author | Helfter, Mathieu |
| author_facet | Helfter, Mathieu |
| contents | For every couple of Hausdorff functions $ ψ$ and $φ$ verifying some mild assumptions, there exists a compact subset $ K $ of the Baire space such that the $ φ$-Hausdorff measure and the $ ψ$-packing measure on $ K$ are both finite and positive. Such examples are then embedded in any infinite dimensional Banach space to answer positively a question of Fan on the existence of metric spaces with arbitrary scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces Helfter, Mathieu Functional Analysis Dynamical Systems Metric Geometry Probability For every couple of Hausdorff functions $ ψ$ and $φ$ verifying some mild assumptions, there exists a compact subset $ K $ of the Baire space such that the $ φ$-Hausdorff measure and the $ ψ$-packing measure on $ K$ are both finite and positive. Such examples are then embedded in any infinite dimensional Banach space to answer positively a question of Fan on the existence of metric spaces with arbitrary scales. |
| title | Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach spaces |
| topic | Functional Analysis Dynamical Systems Metric Geometry Probability |
| url | https://arxiv.org/abs/2502.09643 |