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RESEARCH PRODUCT

Description of the limit set of Henstock–Kurzweil integral sums of vector-valued functions

Diana CaponettiL. Di PiazzaVladimir Kadets

subject

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 functionAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2015-01-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2014.07.050