A generalization of the Bochner integral to locally convex spaces

We present a generalization of the Bochner integral to locally convex spaces. This generalization preserves the nuclearity of the mapping of the space of continuous functions on a compactum represented by the Bochner integral. We introduce locally convex spaces in which the study of a broad class of vector measures with values in these spaces reduces to the study of measures with values in a normed space. The results obtained are used to describe Fréchet spaces possessing the RN property.Translated from Matematicheskie Zametki, Vol. 18, No. 4, pp. 577–588, October, 1975.