A convergence theorem for the Henstock-Kurzweil integral (Q541403)
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scientific article; zbMATH DE number 5904837
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A convergence theorem for the Henstock-Kurzweil integral |
scientific article; zbMATH DE number 5904837 |
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A convergence theorem for the Henstock-Kurzweil integral (English)
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7 June 2011
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The main result says: Let \(V\) be a locally convex Hausdorff space sequentially complete with respect to the weak topology and \(f_n:[a,b]\rightarrow V\) a sequence of HK-equi-integrable functions converging pointwise to \(f\) in the weak topology. Then \(f\) is HK-integrable and \((HK)\int f_n\rightarrow (HK)\int f\) in the weak topology.
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HK-integral
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locally convex spaces
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weak topology
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convergence theorem
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HK-equi-integrable
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