Continuity of convex functions
In this paper, we consider the set V(K) of all convex real-valued functions defined on convex compacts Kс M and find conditions under which all functions fe V(K) are scattered continuous. It is shown that there exist functions fe V(K) that are not Borel, and, for any ordinal а<ю , there are functions fe V(K) that exactly belong to the а th Baire class.
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Keywords
compact, ordinals, Borel sets, extreme points, scattered continuous functions, convex function, компакт, ординалы, борелевские множества, крайние точки, разреженно непрерывная функция, выпуклая функцияAuthors
| Name | Organization | |
| Polukhina Anastasiya Valer'evna | Tomsk State University | spongik@yandex.ru |
| Khmyleva Tatiana Evgenievna | Tomsk State University | TEX2150@yandex.ru |
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Continuity of convex functions | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2013. № 5(25).
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