Covering $L^p$ spaces by balls

Clemente Zanco; Michael Levin; Vladimir P. Fonf

arxiv: 1212.2817 · v1 · pith:GTMIUAYGnew · submitted 2012-12-12 · 🧮 math.FA · math.GN

Covering L^p spaces by balls

Vladimir P. Fonf , Michael Levin , Clemente Zanco This is my paper

classification 🧮 math.FA math.GN

keywords ballscoveringuniformlybanachbelongsclosedexistsgiven

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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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Covering L^p spaces by balls

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