Covering $L^p$ spaces by balls

Vladimir P. Fonf; Michael Levin; Clemente Zanco

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arXiv · 1212.2817

Covering $L^p$ spaces by balls

Vladimir P. Fonf·Michael Levin·Clemente Zanco

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Abstract

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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BibTeX RIS

Vladimir P. Fonf, Michael Levin, Clemente Zanco. 2012-12-12. Covering $L^p$ spaces by balls. https://arxiv.org/abs/1212.2817

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