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Measurable selections in normed spaces

Published online by Cambridge University Press:  20 January 2009

S. J Leese
S. J Leese
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009
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It is sometimes desirable to know in what circumstances a measurable set valued function admits a measurable selector; this problem occurs regularly in the theory of optimal control (see for example (3) and (7)). In this paper we demonstrate the existence of measurable selectors in two particular cases where the choice of selector has a simple geometrical interpretation, namely that of being a “ nearest-point ” selector, as is explained in detail below. This work derives in part from that of C. Castaing, particularly from Théorème 3.4 of (2), of which this is an extension.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 2 , September 1974 , pp. 147 - 150
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

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