The McShane, PU and Henstock integrals of Banach valued functions

DOI10.1023/A:1021736031567zbMath1011.28007OpenAlexW1579188999MaRDI QIDQ4799991

Valeria Marraffa, Luisa Di Piazza

Publication date: 31 March 2003

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/30729

zbMATH Keywords

Pettis integralmultipliersHenstock integralMcShane integralvariational integralsPU integral

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (19)

Gauge integrals and selections of weakly compact valued multifunctions ⋮ The Radon Nikodym property and multipliers of \(\mathcal{HK}\)-integrable functions ⋮ Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures ⋮ Dunford-Henstock-Kurzweil and Dunford-McShane integrals of vector-valued functions defined on \(m\)-dimensional bounded sets ⋮ Solution tube method for impulsive periodic differential inclusions of first order ⋮ Multi-integrals of finite variation ⋮ A Henstock-Kurzweil type integral on one dimensional integral currents ⋮ Relations among gauge and Pettis integrals for \(cwk(X)\)-valued multifunctions ⋮ On the integration of Riemann-measurable vector-valued functions ⋮ A variational Henstock integral characterization of the Radon-Nikodým property ⋮ On summability, integrability and impulsive differential equations in Banach spaces ⋮ An extension of the Birkhoff integrability for multifunctions ⋮ Integration of multifunctions with closed convex values in arbitrary Banach spaces ⋮ Multifunctions determined by integrable functions ⋮ Variational measure with respect to measurable gauges ⋮ On Summability, Multipliability, and Integrability ⋮ A characterization of absolutely summing operators by means of McShane integrable functions ⋮ Properties of the Riemann-Lebesgue integrability in the non-additive case ⋮ Existence theory for semilinear evolution inclusions involving measures

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• The Henstock and McShane integrals of vector-valued functions
• Weak compactness and reflexivity
• An integral defined by approximating $BV$ partitions of unity
• REPRESENTATIONS OF WEAK AND STRONG INTEGRALS IN BANACH SPACES

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