We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ
DI PIAZZA L, MUSIAL K (2006). A decomposition theorem for compact-valued Henstock integral. MONATSHEFTE FÜR MATHEMATIK, 148(2), 119-126 [10.1007/s00605-005-0376-2].
A decomposition theorem for compact-valued Henstock integral
DI PIAZZA, Luisa;
2006-01-01
Abstract
We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ
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