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2007/2008 Asymptotic Structure of Banach Spaces and Riemann Integration
K. M. Naralenkov
Real Anal. Exchange 33(1): 113-126 (2007/2008).


In this paper we focus on the Lebesgue property of Banach spaces. A real Banach space $X$ is said to have the Lebesgue property if any Riemann integrable function from $[0,1]$ into $X$ is continuous almost everywhere on $[0,1]$. We obtain a partial characterization of the Lebesgue property, showing that it has connections with the asymptotic geometry of the space involved.


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K. M. Naralenkov. "Asymptotic Structure of Banach Spaces and Riemann Integration." Real Anal. Exchange 33 (1) 113 - 126, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 28 April 2008

zbMATH: 1151.26008
MathSciNet: MR2402867

Primary: 26A42 , 46B20
Secondary: 28B05 , 46G10

Keywords: asymptotic $\ell^{1}$ Banach space , Lebesgue property , Riemann integral , Schur property , spreading model

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 1 • 2007/2008
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