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Some properties of vector measures taking values in a topological vector space

Published online by Cambridge University Press:  09 April 2009

Efstathios Giannakoulias
Efstathios Giannakoulias
Affiliation:
Department of Mathmatics Section of Mathematical Analysis and its ApplicationsAthens UniversityPanepistemiopolis, 157 81 Athens, Greece
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Abstract

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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 sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 224 - 230
Copyright
Copyright © Australian Mathematical Society 1987

References

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