Corrigendum to Spaces of Vector-Valued Measurable Functions.

Ep de Jonge

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Spaces of Vector-Valued Measurable Functions.

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For Banach-space-valued functions, the concepts of 𝒫-measurability, λ-measurability and m-measurability are defined, where 𝒫 is a δ-ring of subsets of a nonvoid set T, λ is a σ-subadditive submeasure on σ(𝒫) and m is an operator-valued measure on 𝒫. Various characterizations are given for 𝒫-measurable (resp. λ-measurable, m-measurable) vector functions on T. Using them and other auxiliary results proved here, the basic theorems of [6] are rigorously established.

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For multifunctions $F : T \times X \to 2^{Y}$ , measurable in the first variable and semicontinuous in the second one, a relation is established between being product measurable and being superpositionally measurable.