A variational Henstock integral characterization of the Radon-Nikodým property

zbMath1200.46021MaRDI QIDQ2267689

Luisa Di Piazza, Benedetto Bongiorno, Kazimierz Musiał\

Publication date: 1 March 2010

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

Full work available at URL: https://projecteuclid.org/euclid.ijm/1264170840

zbMATH Keywords

Radon-Nikodým propertyfinitely additive measuresHenstock integral Radon-Nikodým theorem

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Radon-Nikodým, Kre?n-Milman and related properties (46B22) Denjoy and Perron integrals, other special integrals (26A39) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (12)

Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis ⋮ Gauge integrals and selections of weakly compact valued multifunctions ⋮ Some new results on integration for multifunction ⋮ Radon-Nikodým theorems for finitely additive multimeasures ⋮ The Radon Nikodym property and multipliers of \(\mathcal{HK}\)-integrable functions ⋮ The average range characterization of the Radon-Nikodym property ⋮ Differentiation of an additive interval measure with values in a conjugate Banach space ⋮ Multi-integrals of finite variation ⋮ Some full characterizations of differentiable functions ⋮ Relations among gauge and Pettis integrals for \(cwk(X)\)-valued multifunctions ⋮ Integration of multifunctions with closed convex values in arbitrary Banach spaces ⋮ Variational measure with respect to measurable gauges

Cites Work

• The Henstock integral for Banach-valued functions
• A new full descriptive characterization of Denjoy-Perron integral
• A descriptive characterization of the Denjoy-Bochner integral and its generalizations
• The Lebesgue and Denjoy-Perron integrals from a descriptive point of view
• Derivates of interval functions
• Variational Measures in the Theory of the Integration in ℝ m
• The McShane, PU and Henstock integrals of Banach valued functions
• NOWHERE WEAK DIFFERENTIABILITY OF THE PETTIS INTEGRAL
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