This article is cited in 3 papers

A generalization of the Bochner integral to locally convex spaces

V. I. Rybakov

Tula State Pedagogical Institute

Abstract: 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.

UDC: 517

Received: 29.10.1973

 English version: Mathematical Notes, 1975, 18:4, 933–938

Bibliographic databases:

• 
•