0000000000519262

AUTHOR

Anna Rita Sambucini

showing 9 related works from this author

Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

2019

The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…

Pure mathematicsIntegrable systemMathematics::Classical Analysis and ODEsBanach spaceselection01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Separable spaceSettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematics0101 mathematicsMathematicsPettis integralMathematics::Functional AnalysisMultifunction Gauge integral Decomposition theorem for multifunction Pettis integral SelectionApplied Mathematics010102 general mathematicsRegular polygonExtension (predicate logic)Gauge (firearms)Functional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsMultifunctionPettis integraldecomposition theorem for multifunctionAnnali di Matematica Pura ed Applicata (1923 -)
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Multifunctions determined by integrable functions

2019

Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.

Pure mathematicsPositive multifunctionIntegrable systemApplied Mathematicsselection02 engineering and technologymultifunction determined by a functionTheoretical Computer ScienceFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional AnalysisPositive multifunction gauge integral selection multifunction determined by a function measure theory.measure theorySettore MAT/05 - Analisi MatematicaArtificial Intelligence020204 information systemsgauge integral0202 electrical engineering electronic engineering information engineeringFOS: Mathematics020201 artificial intelligence & image processingVector-valued functionSoftwareCounterexampleMathematics
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Set-valued Brownian motion

2015

Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the paper of the second author in which an embedding result is obtained which considers also the ordered structure of $ck(X)$ and f-algebras.

Pure mathematicsGeneral MathematicsBanach spaceStructure (category theory)Vector LatticesSpace (mathematics)01 natural sciencesSet (abstract data type)Radstrom embedding theoremMathematics::ProbabilityFOS: MathematicsMarginal distributions0101 mathematicsBrownian motionMathematicsgeneralized Hukuhara differenceApplied MathematicsProbability (math.PR)010102 general mathematicsRegular polygonBrownian motion · Rådström embedding theorem · Vector lattices · Marginal distributions · Generalized Hukuhara difference60J65 58C06 46A40Functional Analysis (math.FA)010101 applied mathematicsMathematics - Functional AnalysisBrownian motion Radstrom embedding theorem Vector Lattices Marginal distributions generalized Hukuhara differenceEmbeddingBrownian motionMarginal distributionMathematics - Probability
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Gauge integrals and selections of weakly compact valued multifunctions

2016

In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered.

Pure mathematicsIntegrable systemSelection (relational algebra)Multifunction; Selection; Set-valued Pettis Henstock and McShane integrals; Analysis; Applied MathematicsSet-valued PettisBanach spaceMathematics::General Topology01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Settore MAT/05 - Analisi MatematicaFOS: Mathematics0101 mathematicsSelectionMathematicsMathematics::Functional AnalysisApplied Mathematics010102 general mathematicsMathematical analysisRegular polygonGauge (firearms)Functional Analysis (math.FA)Henstock and McShane integralsComputer Science::Other010101 applied mathematicsMathematics - Functional AnalysisHyperspaceMultifunctionAnalysisMultifunction set-valued Pettis Henstock and McShane integrals selection
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Convergence for varying measures in the topological case

2023

In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.

Mathematics - Functional Analysis28B05Primary 28B20 Secondary 26E25 26A39 28B05 46G10 54C60 54C6526A39setwise convergence vaguely convergence weak convergence of measures locally compact Hausdorff space Vitali's TheoremSettore MAT/05 - Analisi Matematica54C60FOS: MathematicsPrimary 28B20Secondary 26E2554C65Functional Analysis (math.FA)46G10
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Multi-integrals of finite variation

2020

The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.

Decomposition of multifunctionsFinite variation54C60General Mathematics010102 general mathematics54C6501 natural sciencesFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional Analysis28B0526A3926E25Settore MAT/05 - Analisi MatematicaFinite interval variationFOS: MathematicsDecomposition (computer science)Applied mathematicsMathematics - Functional Analysis; Mathematics - Functional Analysis; 28B20 26E25 26A39 28B05 46G10 54C60 54C6528B200101 mathematicsMultivalued integralMathematics46G10
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Some new results on integration for multifunction

2018

It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.

Pure mathematicsSelection (relational algebra)Integrable systemApplied MathematicsGeneral Mathematics010102 general mathematicsMultifunction set-valued Pettis integral set-valued variationally Henstock and Birkhoff integrals selectionselectionAbsolute continuity01 natural sciencesMeasure (mathematics)Set-valued Pettis integralFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional Analysisset-valued Pettis integral010101 applied mathematicsMultifunctionSettore MAT/05 - Analisi MatematicaHenstock and Birkhoff integralsFOS: Mathematicsset-valued variationally0101 mathematicsSet-valued variationally henstock and birkhoff integralMathematicsRicerche di Matematica
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Integration of multifunctions with closed convex values in arbitrary Banach spaces

2018

Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the "positive multifunctions". Among them an investigation of multifunctions determined by vector-valued functions is presented. Finally, decomposition results are obtained for scalarly and gauge-defined integrals of multifunctions and a full description of McShane integrability in terms of Henstock and Pettis integrability is given.

Mathematics::Functional AnalysisPositive multifunctionPhysics::Medical PhysicsMathematics::Optimization and ControlselectionPositive multifunction gauge integral decomposition theorem for multifunctionselection measure theoryComputer Science::OtherFunctional Analysis (math.FA)Mathematics - Functional Analysismeasure theorySettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematicsdecomposition theorem for multifunction28B20 26E25 26A39 28B0 46G10 54C60 54C65
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Convergence for varying measures

2023

Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.

Convergence in total variationSetwise convergenceConvergence in total variationUniform integrabilityAbsolute integrabilityPettis integralMultifunctionAbsolute integrabilitySetwise convergenceApplied MathematicsFunctional Analysis (math.FA)28B20 26E25 26A39 28B05 46G10 54C60 54C65Mathematics - Functional AnalysisMultifunctionSettore MAT/05 - Analisi MatematicaFOS: MathematicsPettis integralUniform integrabilityAnalysisJournal of Mathematical Analysis and Applications
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