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Selection and representation theorems for $ \sigma $-compact valued multifunctions


Author: S. M. Srivastava
Journal: Proc. Amer. Math. Soc. 83 (1981), 775-780
MSC: Primary 04A15; Secondary 04A05, 54C65, 54H05
DOI: https://doi.org/10.1090/S0002-9939-1981-0630054-7
MathSciNet review: 630054
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Abstract: In this paper we give two applications of results of Shchegolkov and Saint-Raymond on Borel sets with $ \sigma $-compact sections. First we give a sufficient condition under which a partition of a Polish space into $ \sigma $-compact sets admits a Borel cross-section. Then a representation theorem for $ \sigma $-compact valued multifunctions, expressing them as unions of continuously indexed Borel graphs, is proved.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0630054-7
Keywords: Multifunction, partition, selector, cross-section, representation
Article copyright: © Copyright 1981 American Mathematical Society

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