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RESEARCH PRODUCT

Closure properties for integral problems driven by regulated functions via convergence results

Valeria MarraffaBianca SatcoLuisa Di Piazza

subject

Applied Mathematics010102 general mathematicsClosure (topology)Solution set01 natural sciencesMeasure (mathematics)010101 applied mathematicsSettore MAT/05 - Analisi MatematicaConvergence (routing)Bounded variationApplied mathematics0101 mathematicsconvergence Kurzweil-Steltjes integral measure integral equation regulated function bounded variationAnalysisMathematics

description

Abstract In this paper we give necessary and sufficient conditions for the convergence of Kurzweil–Stieltjes integrals with respect to regulated functions, using the notion of asymptotical equiintegrability. One thus generalizes several well-known convergence theorems. As applications, we provide existence and closure results for integral problems driven by regulated functions, both in single- and set-valued cases. In the particular setting of bounded variation functions driving the equations, we get features of the solution set of measure integrals problems.

yearjournalcountryeditionlanguage
2018-10-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2018.06.012