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Descriptive characterizations of Pettis and strongly McShane integrals. (English) Zbl 1298.28025

Characterizations of additive interval functions which are primitives of Pettis or strongly McShane integrable functions in terms of their scalar derivatives were introduced and studied , respectively by K. Naralenkov [Czech. Math. J. 60, No. 3, 737–750 (2010; Zbl 1224.26028)] and S. Schwabik and G. Ye [Topics in Banach space integration. Series in Real Analysis 10. Hackensack, NJ: World Scientific (2005; Zbl 1088.28008)]. In the present paper the author gives further characterizations of these additive interval functions in terms of their average ranges.

MSC:

28B05 Vector-valued set functions, measures and integrals
58C20 Differentiation theory (Gateaux, Fréchet, etc.) on manifolds
46G05 Derivatives of functions in infinite-dimensional spaces
46G10 Vector-valued measures and integration
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