The McShane integral of Banach-valued functions
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Publication:1825980
zbMath0685.28003MaRDI QIDQ1825980
Publication date: 1990
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
Pettis integrable functionBanach-valuedintegral of Riemann-typeMcShane integral of functions mapping a closed interval into a real Banach space.
Vector-valued set functions, measures and integrals (28B05) Integrals of Riemann, Stieltjes and Lebesgue type (26A42)
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Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions ⋮ On the limits of the generalization of the Kolmogorov integral ⋮ A note on comparisons between Birkhoff and McShane-type integrals for multifunctions ⋮ The McShane integral in weakly compactly generated spaces ⋮ On Henstock--Kurzweil and McShane integrals of Banach space-valued functions ⋮ The weak McShane integral ⋮ Integration in Hilbert generated Banach spaces ⋮ Dunford-Henstock-Kurzweil and Dunford-McShane integrals of vector-valued functions defined on \(m\)-dimensional bounded sets ⋮ Some remarks on descriptive characterizations of the strong McShane integral ⋮ Henstock and McShane integrals for Banach-valued functions ⋮ A Lusin type measurability property for vector-valued functions ⋮ The new extensions of the Henstock-Kurzweil and the McShane integrals of vector-valued functions ⋮ On the integration of Riemann-measurable vector-valued functions ⋮ Non absolutely convergent integrals of functions taking values in a locally convex space ⋮ On Henstock integral of fuzzy-number-valued functions. I ⋮ On the Henstock-Kurzweil-Dunford and Kurzweil-Henstock-Pettis integrals ⋮ Riemann type integrals for functions taking values in a locally convex space ⋮ The set of solutions of Volterra and Urysohn integral equations in Banach spaces ⋮ The Denjoy extension of the Riemann and Mcshane integrals ⋮ The Henstock-Kurzweil-Pettis Integrals and Existence Theorems for the Cauchy Problem ⋮ A new fuzzy McShane integrability ⋮ A new result on impulsive differential equations involving non-absolutely convergent integrals ⋮ On the equivalence of McShane and Pettis integrability in non-separable Banach spaces ⋮ On the equivalence of McShane and Pettis integrability in non-separable Banach spaces ⋮ New extension of the variational McShane integral of vector-valued functions ⋮ Variations and variational measures in integration theory and some applications ⋮ A characterization of absolutely summing operators by means of McShane integrable functions ⋮ Approximating Bochner integrals by Riemann sums ⋮ On the Strong McShane Integral of Functions with Values in a Banach Space
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