Integrable and absolutely continuous vector-valued functions. (English) Zbl 1516.28006

Lewis, Andrew D.

Rocky Mt. J. Math. 52, No. 3, 925-947 (2022).

Let \(\left( X,\mathcal{A},\mu \right) \) be a complete \(\sigma \)-finite measure space and \(\left( V,\mathcal{O}\right) \) be a Hausdorff locally convex topological \(F\)-vector space, \(F\in \left\{ \mathbb{R},\mathbb{C} \right\} \). In the paper the author develop a theory of integrability of functions \(f:X\rightarrow V\). The approach follows similar lines as in the case of the Banach spaces for the Bochner and Pettis integrals.

Reviewer: Dumitrŭ Popa (Constanţa)

MSC:

28B05	Vector-valued set functions, measures and integrals
46A32	Spaces of linear operators; topological tensor products; approximation properties

Keywords:

locally convex spaces; integration; differentiation

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