Open Access
2013/2014 Riemann and Riemann-type Integration in Banach Spaces
Sk. Jaker Ali, Pratikshan Mondal
Real Anal. Exchange 39(2): 403-440 (2013/2014).


Riemann, Riemann-Dunford, Riemann-Pettis and Darboux integrable functions with values in a Banach space and Riemann-Gelfand integrable functions with values in the dual of a Banach space are studied in the light of the work of Graves, Alexiewicz and Orlicz, and Gordon. Various properties of these types of integrals and the interrelation between them are established. The Fundamental Theorem of Integral Calculus for these types of integrals is also studied.


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Sk. Jaker Ali. Pratikshan Mondal. "Riemann and Riemann-type Integration in Banach Spaces." Real Anal. Exchange 39 (2) 403 - 440, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 30 June 2015

zbMATH: 1326.26018
MathSciNet: MR3365383

Primary: 26A42 , 28B05
Secondary: 46G10

Keywords: Bochner integrable equivalent. , Darboux integral , Riemann integral , Riemann-Dunford integral , Riemann-Gelfand integral , Riemann-Pettis integral

Rights: Copyright © 2014 Michigan State University Press

Vol.39 • No. 2 • 2013/2014
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