Search results for "Henstock–Kurzweil integral"

showing 7 items of 7 documents

Derivatives not first return integrable on a fractal set

2018

We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.

Pure mathematicss-dimensional Hausdorff measureIntegrable systemApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicss-setFirst return integrals-derivative01 natural sciences010305 fluids & plasmasSettore MAT/05 - Analisi Matematica0103 physical sciencesFractal set0101 mathematicsAlgebra over a fieldHenstock–Kurzweil integralMathematics
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Description of the limit set of Henstock–Kurzweil integral sums of vector-valued functions

2015

Abstract Let f be a function defined on [ 0 , 1 ] and taking values in a Banach space X . We show that the limit set I HK ( f ) of Henstock–Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.

Discrete mathematicsHenstock–Kurzweil integralApplied MathematicsMathematics::Classical Analysis and ODEsBanach spaceRiemann integralFunction (mathematics)Separable spacesymbols.namesakeSettore MAT/05 - Analisi MatematicaImproper integralsymbolsHenstock–Kurzweil integral Limit set of integral sums Multifunction Aumann integralLimit setVector-valued functionAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Decomposability in the space ofHKP-integrable functions

2014

In this paper we introduce the notion of decomposability in the space of Henstock-Kurzweil-Pettis integrable (for short HKP-integrable) functions. We show representations theorems for decomposable sets of HKP-integrable or Henstock integrable functions, in terms of the family of selections of suitable multifunctions.

Discrete mathematicsPure mathematicsHenstock–Kurzweil integralIntegrable systemGeneral MathematicsSpace (mathematics)MathematicsMathematische Nachrichten
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Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis

2011

Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(t)dt be a finitely additive interval measure on the unit interval [0, 1], where the integrals are taken in the sense of Henstock–Kurzweil. Necessary and sufficient conditions are given for Φ to be the indefinite integral of a Henstock–Kurzweil–Pettis (or Henstock, or variational Henstock) integrable function f:[0, 1] → X.

Pettis integralDiscrete mathematicsPure mathematicsHenstock–Kurzweil integralApplied MathematicsGeneral MathematicsBanach spaceMeasure (mathematics)Schauder basisRadon–Nikodym theoremSettore MAT/05 - Analisi MatematicaHenstock-Kurzweil integral Henstock-Kurzweil-Pettis integral Henstock integral variational Henstock integral Pettis integralLocally integrable functionMathematicsUnit intervalActa Mathematica Sinica, English Series
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Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space

2009

Abstract A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.

Metric spaceHenstock–Kurzweil integralGeneral MathematicsInjective metric spaceMathematical analysisMetric (mathematics)Measure (physics)Pseudometric spaceType (model theory)MathematicsConvex metric spacegmj
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Radon–Nikodým Theorems for Finitely Additive Multimeasures

2015

In this paper we deal with interval multimeasures. We show some Radon–Nikodým theorems for such multimeasures using multivalued Henstock or Henstock–Kurzweil–Pettis derivatives. We do not use the separability assumption in the results.

Pure mathematicsHenstock–Kurzweil integralchemistrySettore MAT/05 - Analisi MatematicaApplied MathematicsMathematical analysischemistry.chemical_elementRadonMultifunction Henstock–Kurzweil integral Henstock–Kurzweil–Pettis integral selection Radon–Nikodým theoremAnalysisSelection (genetic algorithm)Mathematics
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A new full descriptive characterization of Denjoy-Perron integral

1995

It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.

Pure mathematicsHenstock–Kurzweil integralMathematical analysisMeasure (physics)Riemann integralFunction (mathematics)Absolute continuitysymbols.namesakesymbolsAlmost everywhereGeometry and TopologyDaniell integralDifferentiable functionAnalysisMathematics
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