Geodesic
Continuity of convex functions
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 26-29

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In this paper, we consider the set $V(K)$ of all convex real-valued functions defined on convex compacts $K\subset\mathbb R^n$ and find conditions under which all functions $f\in V(K)$ are scattered continuous. It is shown that there exist functions $f\in V(K)$ that are not Borel, and, for any ordinal $\alpha\omega_1$, there are functions $f\in V(K)$ that exactly belong to the $\alpha$th Baire class.
Keywords: convex function, scattered continuous functions, extreme points, Borel sets, ordinals, compact. 
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     author = {A. V. Polukhina and T. E. Khmyleva},
     title = {Continuity of convex functions},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {26--29},
     publisher = {mathdoc},
     number = {5},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_5_a2/}
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A. V. Polukhina; T. E. Khmyleva. Continuity of convex functions. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 5 (2013), pp. 26-29. http://geodesic.mathdoc.fr/item/VTGU_2013_5_a2/