Search results for "Bochner integral"

showing 5 items of 5 documents

An integral for a banach valued function

2009

Abstract Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.

Discrete mathematicsBanach valued function (PU)-partition (PU)*-integral Bochner-integralGeneral MathematicsInfinite-dimensional vector functionBochner integralRiemann–Stieltjes integralRiemann integralBochner spaceExponential integralsymbols.namesakeSettore MAT/05 - Analisi MatematicasymbolsPaley–Wiener integralDaniell integralMathematicsTatra Mountains Mathematical Publications
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On some parameters related to weak noncompactness in L1(μ,E)

2009

Abstract A weak measure of noncompactness γU is defined in a Banach space in terms of convex compactness. We obtain relationships between the measure γU (A) of a bounded set A in the Bochner space L1 (μ,E) and two parameters Π(A) and Δ1(A). Then the criterion for relative weak compactness due to Ulger [19] and Diestel-Ruess-Schachermayer [11] is recovered.

Discrete mathematicsMathematics (miscellaneous)Compact spaceBounded setBochner integralRegular polygonBanach spaceBochner spaceMeasure (mathematics)MathematicsQuaestiones Mathematicae
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On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

2011

The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.

Pettis integralSet (abstract data type)Mathematics::Functional AnalysisPure mathematicsIntegrable systemBounded functionBanach latticeBochner integralBanach spaceEmbeddingAbsolutely summing operator Banach lattice Bochner integral Pettis integral cone absolutely summing operator integrably bounded set- valued function set-valued operator.Mathematics
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A Riemann sums method in the Theory of vector Integration

2010

Settore MAT/05 - Analisi MatematicaRiemann sum Bochner integral Pettis integral
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A first return examination of vector valued integrals.

2009

We prove that for each Bochner integrable function f there exists a trajectory yielding the Bochner integral of f, and that on infinite dimensional Banach spaces there exist Pettis integrable functions f such that no trajectory yields the Pettis integral of f.

Trajectory first return integral Bochner integral Pettis integral McShane integral.Settore MAT/05 - Analisi Matematica
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