Search results for "s-HK Integral"

showing 3 items of 3 documents

An Henstock-Kurzweil type integral on a meausure metric space

2014

We consider an Henstock-Kurzweil type integral defined on a complete measure metric space $X=(X, d)$ endowed with a Radon measure $\mu$ and with a family $\F$ of ``intervals" that satisfies, besides usual conditions, the Vitali covering theorem. In particular, for such integral, we obtain extensions of the descriptive characterization of the classical Henstock-Kurzweil integral on the real line, in terms of $ACG_*$ functions and in terms of variational measures. Moreover we show that, besides the usual Henstock-Kurzweil integral on the real line, such integral includes also the dyadic Henstock-Kurzweil integral, the $GP$-integral and the $s$-HK integral. For this last integral we prove a be…

Settore MAT/05 - Analisi Matematica$ACG^\bigtriangleup$s-sets-HK integral.$\mu$-HK integralcritical variation
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ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS

2015

The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.

Differentiation under the integral signReal analysisFundamental theoremApplied Mathematicss-SetMathematics::Classical Analysis and ODEss-HK IntegralDifferential calculusTime-scale calculusIntegration by substitutionAlgebraSettore MAT/05 - Analisi MatematicaModeling and SimulationFundamental theorem of calculusFunctions Hs-ACGδ.CalculusGeometry and TopologyGradient theoremMathematicsFractals
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The Henstock-Kurzweil-Stieltjes type integral for real functions on a fractal subset of the real line

2011

The aim of this paper is to introduce an Henstock-Kurzweil type integration process for real functions on a fractal subset E of the real line.

Settore MAT/05 - Analisi Matematicas-HK integrals-setHausdorff measure
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