Search results for "critical variation"

showing 2 items of 2 documents

An Integral on a Complete Metric Measure Space

2015

We study a Henstock-Kurzweil type integral defined on a complete metric measure space \(X\) endowed with a Radon measure \(\mu\) and with a family of “cells” \(\mathcal{F}\) that satisfies the Vitali covering theorem with respect to \(\mu\). This integral encloses, in particular, the classical Henstock-Kurzweil integral on the real line, the dyadic Henstock-Kurzweil integral, the Mawhin’s integral [19], and the \(s\)-HK integral [4]. The main result of this paper is the extension of the usual descriptive characterizations of the Henstock-Kurzweil integral on the real line, in terms of \(ACG^*\) functions (Main Theorem 1) and in terms of variational measures (Main Theorem 2).

HK-integralMeasure (physics)Space (mathematics)26A39Settore MAT/05 - Analisi MatematicaMetric (mathematics)CalculusGeometry and Topology28A12HK-integral ACG4 function critical variationAnalysis\(ACG^\bigtriangleup\) functionMathematicscritical variation
researchProduct

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
researchProduct