The integration theory of Banach space valued measures and the Tonelli- Fubini theorems. II: Pettis integration

DOI10.1016/0001-8708(89)90035-2zbMath0770.28007OpenAlexW2039489291MaRDI QIDQ2368025

P. R. Masani, Hannu Niemi

Publication date: 18 August 1993

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(89)90035-2

zbMATH Keywords

Pettis integrabilityGelfand integrabilitysets with finite semi-variationsvariations of a vector measurevector extensions of the Tonelli and Fubini theorems

Mathematics Subject Classification ID

Integration with respect to measures and other set functions (28A25) Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10)

Related Items (18)

On integration with respect to LCTVS-valued finitely additive measures ⋮ Factorizing operators on Banach function spaces through spaces of multiplication operators ⋮ Associate space with respect to a locally \(\sigma \)-finite measure on a \(\delta \)-ring and applications to spaces of integrable functions defined by a vector measure ⋮ OPTIMAL EXTENSIONS FOR POSITIVE ORDER CONTINUOUS OPERATORS ON BANACH FUNCTION SPACES ⋮ Optimal extensions for \(p\)th power factorable operators ⋮ Integration of vector-valued functions with respect to vector measures defined on \(\delta \)-rings ⋮ The Köthe dual of an abstract Banach lattice ⋮ Unnamed Item ⋮ Uo-convergence and its applications to Cesàro means in Banach lattices ⋮ Optimal domain for the Hardy operator ⋮ Optimal extension of positive order continuous operators with values in quasi-Banach lattices ⋮ On the Banach lattice structure of \(L^1_w\) of a vector measure on a \(\delta \)-ring ⋮ A note on real interpolation of \(L^p\)-spaces of vector measures on \(\delta\)-rings ⋮ Complex interpolation of \(L^p\)-spaces of vector measures on \(\delta\)-rings ⋮ Kantorovich-Wright integration and representation of vector lattices ⋮ On the optimally defined Hardy operator in $L^p$-spaces ⋮ Reflexivity of function spaces associated to a \(\sigma\)-finite vector measure ⋮ Integration for Positive Measures with Values in Quasi-Banach Lattices

Cites Work

• L'intégration par rapport à une mesure de Radon vectorielle
• Integration with respect to vector measures
• On integrability and summability in vector spaces
• The theory of stationary vector-valued measures over R.
• Measurability and Pettis integration in Hilbert spaces.
• Stationary vector measures and positive definite translation invariant bimeasures
• On Integration in Vector Spaces
• Functional Operators (AM-21), Volume 1
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