Covering $L^p$ spaces by balls
We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of positive radius, some point exists in $X$ which belongs to infinitely many balls.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We prove that, given any covering of any separable infinite-dimensional
uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of
positive radius, some point exists in $X$ which belongs to infinitely many
balls. |
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| DOI: | 10.48550/arxiv.1212.2817 |