Riemann integration in Banach spaces. (English) Zbl 0764.28008

Gordon, Russell

Rocky Mt. J. Math. 21, No. 3, 923-949 (1991).

This paper contains a clear and interesting exposition of several questions related with the Riemann integration of functions mapping (bounded) closed intervals into Banach spaces. One of the main focuses of the paper is to analyse the Banach spaces having the property of Lebesgue (i.e., those spaces having the property that every Riemann integrable function is continuous almost everywhere on the interval). Also it is examined the relationship between the Riemann integral (in Banach spaces) and other (vector-valued) integrals.
Most of the results in this paper are a compilation of works of Graves, Alexiewicz and Orlicz, Rejouani, Nemirovski, Ochan and Rejouani, and da Rocha. Some of the proves presented here are simpler than the original ones.

Reviewer: P.Jiménez Guerra (Madrid)

MSC:

28B05	Vector-valued set functions, measures and integrals
46G10	Vector-valued measures and integration

Keywords:

measurable function; vector-valued integral; Riemann integral; Banach spaces

References:

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