A convergence theorem for the Henstock-Kurzweil integral. (English) Zbl 1222.28022

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.
Reviewer: Hans Weber (Udine)


28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
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