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.

Luisa Di Piazza, V.M. (2018). Closure properties for integral problems driven by regulated functions via convergence results. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 466(1), 690-710 [10.1016/j.jmaa.2018.06.012].

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

Luisa Di Piazza;Valeria Marraffa
;
2018

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.
Settore MAT/05 - Analisi Matematica
Luisa Di Piazza, V.M. (2018). Closure properties for integral problems driven by regulated functions via convergence results. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 466(1), 690-710 [10.1016/j.jmaa.2018.06.012].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/290873
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