Real Analysis Exchange

Asymptotic Structure of Banach Spaces and Riemann Integration

K. M. Naralenkov

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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.

Article information

Real Anal. Exchange, Volume 33, Number 1 (2007), 113-126.

First available in Project Euclid: 28 April 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 46B20: Geometry and structure of normed linear spaces
Secondary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]

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


Naralenkov, K. M. Asymptotic Structure of Banach Spaces and Riemann Integration. Real Anal. Exchange 33 (2007), no. 1, 113--126.

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