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Omega-Polish spaces and measurable selections

Published online by Cambridge University Press:  09 April 2009

Le Van Tu
Le Van Tu
Affiliation:
Murdoch University, Murdoch, 6153, Western Australia.
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Abstract

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In this paper, the author introduces the notion of Ω-Polish spaces (which includes the Polish spaces and a large class of Banach spaces) and extends Castaing's selection theorem (1966) for closed-valued measurable thin multifunctions from a measurable space into an Ω-Polish space. He also extends Robertson's theorem (1974) in the same way.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 257 - 265
Copyright
Copyright © Australian Mathematical Society 1977

References

Castaing, C. (1966), ‘Quelques problèmes de mesurabilité liés à la théorie de la commande’, C. R. Acad. Sc., Paris, 262, 409–411.Google Scholar
Choquet, G. (1969), Lectures on Analysis, Vol. I (W.A. Benj., New York, 1969).Google Scholar
Himmelberg, C. J. and Van Vleck, F. S. (1969), ‘Some selection theorems for measurable functions’, Can. J. Math. 21, 394–399.CrossRefGoogle Scholar
Kuratowski, K. and Ryll-Nardzewski, C. (1965), ‘A general theorem on selectors’, Bull. Acad. Polon. Math., Astr., Phys., 13, 397–403.Google Scholar
McShane, E. J. and Warfield, R. B. Jr, (1967), ‘On Filipov's implicit functions lemma’, Proc. Amer. Math. Soc., 18, 41–47.Google Scholar
Robertson, A. P. (1974), ‘On measurable selections’, Proc. R. Soc. Edinburgh, 72, 1–7.CrossRefGoogle Scholar
Rogers, C. A. (1970), Hausdorff measures (Cambridge, Univ. Press, page 44).Google Scholar
Singer, I. (1970), Bases in Banach spaces, Vol. I (Springer, New York, 1970).Google Scholar