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

Kaliaj, Sokol B.

Real Anal. Exch. 39(2013-2014), No. 1, 227-238 (2014).

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.

Reviewer: Srinivasa Swaminathan (Halifax)

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

Keywords:

Pettis integral; strongly McShane integral; absolute continuity

Citations:

Zbl 1224.26028; Zbl 1088.28008