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The range of a multimeasure

Published online by Cambridge University Press:  09 April 2009

Le Van Tu
Le Van Tu
Affiliation:
Department of Mathematics University of Western Australia Nedlands 6009 Australia
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Abstract

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In this paper, the author generalizes the concept of thinness introduced by Kingman and Robertson (1968) to study the convexity of the range of a multimeasure. It is proved that every thin multimeasure taking values in a Fréchet space has convex range, and that, for a suitable measureable space, if a multimeasure is non-atomic, then the weak closure of its range is convex.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 4 , December 1978 , pp. 442 - 452
Copyright
Copyright © Australian Mathematical Society 1978

References

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