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1999/2000 A Generalized Riemann Integral for Banach-Valued Functions
Jean-Christophe Feauveau
Real Anal. Exchange 25(2): 919-930 (1999/2000).


We shall develop the properties of an integral for Banach-valued functions. The formalism is the generalized Riemann integral introduced by Kurzweil \cite{Kur} and Henstock \cite{Hen}. More precisely, the presentation is close to the McShane approach \cite{McS}. Besides its simplicity of presentation, four advantages characterize this theory: %{\leftskip=1cm \item{(i)} the definition can be used for real-valued functions, and can be generalized without modification to general real and complex Banach spaces; \item{(ii)} when a function is integrable its norm is also integrable, and the proof is straightforward from the definition; \item{(iii)} for finite dimension spaces the theory is equivalent to the McShane's theory, which is itself equivalent to the Lebesgue's theory; \item{(iv)} and lastly, for general Banach space, we can prove the equivalence to the Bochner's theory. \par%}


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Jean-Christophe Feauveau. "A Generalized Riemann Integral for Banach-Valued Functions." Real Anal. Exchange 25 (2) 919 - 930, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 3 January 2009

zbMATH: 1022.28004
MathSciNet: MR1778543

Primary: 26A39 , 28B05

Keywords: Bochner integral , McShane integral , vector-valued integral

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 2 • 1999/2000
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