Covering Lp Spaces by Balls

Covering Lp 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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Veröffentlicht in:The Journal of geometric analysis 2014, Vol.24 (4), p.1891-1897
Hauptverfasser: Fonf, Vladimir P., Levin, Michael, Zanco, Clemente
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
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Beschreibung
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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-013-9400-2