The generalized McShane integral

zbMath0810.28006MaRDI QIDQ1342694

D. H. Fremlin

Publication date: 4 April 1995

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Pettis integralMcShane integralconvergence theoremsBochner integrable functionsgauge integralgeneralized McShane partitionTalagrand integralvector integration

Mathematics Subject Classification ID

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

Related Items (34)

Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions ⋮ Absolutely summing operators and integration of vector-valued functions ⋮ On the existence of Pettis integrable functions which are not Birkhoff integrable ⋮ A note on comparisons between Birkhoff and McShane-type integrals for multifunctions ⋮ The McShane integral in weakly compactly generated spaces ⋮ The weak McShane integral ⋮ Integration in Hilbert generated Banach spaces ⋮ Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures ⋮ On lineability in vector integration ⋮ Multipliers of variationally McShane integrable functions in locally convex space ⋮ 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 ⋮ 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 ⋮ Multiplication operators in Köthe-Bochner spaces ⋮ Riemann type integrals for functions taking values in a locally convex space ⋮ On integration of vector functions with respect to vector measures ⋮ Pointwise limits of Birkhoff integrable functions ⋮ An extension of the Birkhoff integrability for multifunctions ⋮ Integration of multifunctions with closed convex values in arbitrary Banach spaces ⋮ Multifunctions determined by integrable functions ⋮ A new fuzzy McShane integrability ⋮ 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 ⋮ A remark on weak McShane integral ⋮ The multiplier for the weak McShane integral ⋮ New extension of the variational McShane integral of vector-valued functions ⋮ Open problems in Banach spaces and measure theory ⋮ A characterization of absolutely summing operators by means of McShane integrable functions ⋮ The variational McShane integral in locally convex spaces ⋮ On coincidence of Pettis and McShane integrability ⋮ Convergence for varying measures ⋮ Approximating Bochner integrals by Riemann sums

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