J Austral Math Soc Ser A 43 pp224--230, 1987.

Some Properties of Vector Measures Taking Values in a Topological Vector Space

Efstathios Giannakoulias

Abstract

In this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function f: S ® E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a seqentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.

1980 AMS Subject Classification: 38B05

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Authors

Efstathios Giannakoulias

Department of Mathematics, Section of Mathematical Analysis and its Applications, Athens University, Panepistemiopolis, 157 81 Athens, Greece.