Search results for "Riemann–Stieltjes integral"

showing 10 items of 11 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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A Constructive Minimal Integral which Includes Lebesgue Integrable Functions and Derivatives

2000

In this paper we provide a minimal constructive integration process of Riemann type which includes the Lebesgue integral and also integrates the derivatives of differentiable functions. We provide a new solution to the classical problem of recovering a function from its derivative by integration, which, unlike the solution provided by Denjoy, Perron and many others, does not possess the generality which is not needed for this purpose.The descriptive version of the problem was treated by A. M. Bruckner, R. J. Fleissner and J. Foran in [2]. Their approach was based on the trivial observation that for the required minimal integral, a function F is the indefinite integral of f if and only if F'…

Discrete mathematicssymbols.namesakeDifferentiation of integralsGeneral MathematicssymbolsRiemann–Stieltjes integralLocally integrable functionRiemann integralDaniell integralDifferentiable functionLebesgue integrationLebesgue–Stieltjes integrationMathematicsJournal of the London Mathematical Society
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Generality of Henstock-Kurzweil type integral on a compact zero-dimensional metric space

2011

ABSTRACT A Henstock-Kurzweil type integral on a compact zero-dimensional metric space is investigated. It is compared with two Perron type integrals. It is also proved that it covers the Lebesgue integral.

General MathematicsInjective metric spaceMathematical analysisLebesgue's number lemmaHenstock-kurzweil integral Perron integral derivation basisRiemann–Stieltjes integralRiemann integralLebesgue integrationVolume integralsymbols.namesakeDifferentiation of integralsSettore MAT/05 - Analisi MatematicasymbolsDaniell integralMathematics
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Henstock type integral in harmonic analysis on zero-dimensional groups

2006

AbstractA Henstock type integral is defined on compact subsets of a locally compact zero-dimensional abelian group. This integral is applied to obtain an inversion formula for the multiplicative integral transform.

Henstock integralApplied MathematicsMathematical analysisLine integralRiemann integralRiemann–Stieltjes integralSingular integralLocally compact groupHenstock–Fourier seriesVolume integralsymbols.namesakeLocally compact zero-dimensional abelian groupImproper integralsymbolsCharacters of a groupInversion formulaDaniell integralMultiplicative integral transformAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A Riemann-Type Integral on a Measure Space

2005

In a compact Hausdorff measure space we define an integral by partitions of the unity and prove that it is nonabsolutely convergent.

Lebesgue measureMathematical analysisMeasure (physics)Mathematics::General Topologypartition of unityRiemann integralRiemann–Stieltjes integralLebesgue integration$PU^*$-integralsymbols.namesakeTransverse measureDifferentiation of integralssymbolsGeometry and TopologyDaniell integral28A25Borel measureAnalysisMathematicsReal Analysis Exchange
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Set valued Kurzweil-Henstock-Pettis integral

2005

It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.

Pettis integralKurzweil–Henstock integralMathematics::Functional AnalysisPure mathematicsGeneralizationApplied MathematicsMathematical analysisKurzweil–Henstock–Pettis integralMathematics::Classical Analysis and ODEsRegular polygonselectionRiemann–Stieltjes integralRiemann integralSupport functionLebesgue integrationsupport functionsymbols.namesakemultifunctionPettis set-valued integralsymbolsMathematics::Metric GeometryDaniell integralAnalysisMathematics
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A Birkhoff type integral and the Bourgain property in a locally convex space

2007

An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.

Pettis integralMcShane integralPure mathematicsMathematical analysisConvex setlocally convex spaceRiemann–Stieltjes integralRiemann integralSingular integral28B05symbols.namesakePettis integral McShane integral Birkho integral locally convex spacesBounded functionPettis integralsymbolsPaley–Wiener integralGeometry and TopologyDaniell integralAnalysisBirkhoff integral46G10Mathematics
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Kurzweil-Henstock type integration on Banach spaces

2004

In this paper properties of Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrals for vector-valued functions are studied. In particular, the absolute integrability for Kurzweil-Henstock integrable functions is characterized and a Kurzweil-Henstock version of the Vitali Theorem for Pettis integrable functions is given.

Pure mathematicsIntegrable systemequiintegrabilityInfinite-dimensional vector functionMathematical analysisBanach spaceRiemann–Stieltjes integralType (model theory)Infinite-dimensional holomorphyKurzweil-Henstock integral28B0526A39Pettis integralGeometry and TopologyDaniell integralLp spaceAnalysisMathematics
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Set-valued stochastic integral equations driven by martingales

2012

Abstract We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.

Stratonovich integralContinuous-time stochastic processApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISStochastic calculusRiemann–Stieltjes integralRiemann integralsymbols.namesakeQuantum stochastic calculusImproper integralsymbolsDaniell integralAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A Stieltjes Approach to Static Hedges

2014

Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be exte…

symbols.namesakeGeneralized functionLebesgue measureDirect methodMathematical analysisBounded variationStochastic gamesymbolsApplied mathematicsRiemann–Stieltjes integralAbsolute continuityLebesgue integrationMathematics
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