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2006/2007 Infinite Dimensional Banach Space of Besicovitch Functions
Jozef Bobok
Real Anal. Exchange 32(2): 319-334 (2006/2007).


Let $C([0,1])$ be the set of all continuous functions mapping the unit interval $[0,1]$ into $\mathbb{R}$. A function $f\in C([0,1])$ is called Besicovitch if it has nowhere one-sided derivative (finite or infinite). We construct a set $\mathcal{B}_{\sup}\negthickspace\subset C([0,1])$ such that $(\mathcal{B}_{\sup},\vert\vert~\vert\vert_{\sup})$ is an infinite dimensional Banach (sub)space in C([0,1]) and each nonzero element of $\mathcal{B}_{\sup}$ is a Besicovitch function.


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Jozef Bobok. "Infinite Dimensional Banach Space of Besicovitch Functions." Real Anal. Exchange 32 (2) 319 - 334, 2006/2007.


Published: 2006/2007
First available in Project Euclid: 3 January 2008

zbMATH: 1213.46024
MathSciNet: MR2369847

Primary: 26A27

Keywords: Besicovitch function , infinite dimensional Banach spac

Rights: Copyright © 2006 Michigan State University Press

Vol.32 • No. 2 • 2006/2007
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