6533b7d0fe1ef96bd125af2e

RESEARCH PRODUCT

Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

Kazimierz MusiałLuisa Di PiazzaAnna Rita SambuciniDomenico Candeloro

subject

Pure mathematicsIntegrable systemMathematics::Classical Analysis and ODEsBanach spaceselection01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Separable spaceSettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematics0101 mathematicsMathematicsPettis integralMathematics::Functional AnalysisMultifunction Gauge integral Decomposition theorem for multifunction Pettis integral SelectionApplied Mathematics010102 general mathematicsRegular polygonExtension (predicate logic)Gauge (firearms)Functional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsMultifunctionPettis integraldecomposition theorem for multifunction

description

The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, together with an extension of a well-known theorem of Fremlin.

yearjournalcountryeditionlanguage
2019-12-04Annali di Matematica Pura ed Applicata (1923 -)
https://doi.org/10.1007/s10231-017-0674-z