The Birkhoff integral and the property of Bourgain

DOI10.1007/s00208-004-0581-7zbMath1061.28006OpenAlexW1558456818MaRDI QIDQ1772069

José Rodríguez, Bernardo Cascales

Publication date: 15 April 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-004-0581-7

zbMATH Keywords

Pettis integralRadon-Nikodým propertyBochner integralBirkhoff integralBourgain property

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10) Radon-Nikodým, Kre?n-Milman and related properties (46B22)

Related Items (25)

Absolutely summing operators and integration of vector-valued functions ⋮ SCALAR BOUNDEDNESS OF VECTOR-VALUED FUNCTIONS ⋮ On the existence of Pettis integrable functions which are not Birkhoff integrable ⋮ Gauge integrals and selections of weakly compact valued multifunctions ⋮ Some new results on integration for multifunction ⋮ Birkhoff integral for multi-valued functions ⋮ A note on comparisons between Birkhoff and McShane-type integrals for multifunctions ⋮ Integration in Hilbert generated Banach spaces ⋮ Linear operators associated with \(p\)-Dunford, \(p\)-Pettis and \(p\)-Bochner integrable functions with values in a Banach space ⋮ On lineability in vector integration ⋮ A convergence theorem for the Birkhoff integral ⋮ A Lusin type measurability property for vector-valued functions ⋮ Multiplication operators in Köthe-Bochner spaces ⋮ On integration of vector functions with respect to vector measures ⋮ Pointwise limits of Birkhoff integrable functions ⋮ A vector Girsanov result and its applications to conditional measures via the Birkhoff integrability ⋮ An extension of the Birkhoff integrability for multifunctions ⋮ Convergence theorems for the Birkhoff integral ⋮ On Birkhoff integrability for scalar functions and vector measures ⋮ SOME EXAMPLES IN VECTOR INTEGRATION ⋮ Properties of the Riemann-Lebesgue integrability in the non-additive case ⋮ Almost everywhere convergent sequences of weak∗‐to‐norm continuous operators ⋮ Distances to spaces of measurable and integrable functions ⋮ Spaces of vector functions that are integrable with respect to vector measures ⋮ Comparison between Birkhoff integral and Gould integral

Cites Work

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• On functions that are universally Pettis integrable
• The Glivenko-Cantelli problem
• On the integration of vector-valued functions
• The Henstock and McShane integrals of vector-valued functions
• Pettis integral and measure theory
• Some topological and geometrical structures in Banach spaces
• On the weak*-Radon Nikodym property
• Integration of Functions with Values in a Bananch Space
• On Integration in Vector Spaces
• Integration in a Convex Linear Topological Space

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