Strong vector valued integrals

Abstract

Strong Bochner type integrals with values in locally convex spaces are introduced. It is shown that the strong integral exists in the same cases as the weak (Gelfand-Pettis) integral is known to exist. The strong integral has better continuity properties that the weak integral.

The paper has been withdrawn, as it has become part of the paper: Two applications of nets, http://arxiv.org/abs/1403.3207