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Sections, selections and Prohorov's theorem |
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| Authors: | Valentin Gutev Vesko Valov |
| Institution: | aSchool of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa;bDepartment of Computer Science and Mathematics, Nipissing University, 100 College Drive, PO Box 5002, North Bay, ON P1B 8L7, Canada |
| Abstract: | The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for l.s.c. mappings. A similar approach works when sieve-complete spaces are considered. |
| Keywords: | Set-valued mapping Lower semi-continuous Upper semi-continuous Selection Section Radon probability measure |
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