Riemann and Riemann-type Integration in Banach Spaces

Abstract

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.