Displaying similar documents to “A continuity in the weak topologies of a vector integral operator.”

Inserting measurable functions precisely

Javier Gutiérrez García, Tomasz Kubiak (2014)

Czechoslovak Mathematical Journal

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A family of subsets of a set is called a σ -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A σ -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect σ -topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a σ -topological version...

A generalized Pettis measurability criterion and integration of vector functions

I. Dobrakov, T. V. Panchapagesan (2004)

Studia Mathematica

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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.