Covering \(L^p\) spaces by balls

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.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2012-12
Hauptverfasser: Fonf, Vladimir P, Levin, Michael, Zanco, Clemente
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Closed balls
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
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:2331-8422