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Proceedings of the American Mathematical Society

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The weak Dirichlet problem for Baire functions


Author: Jirí Spurny
Journal: Proc. Amer. Math. Soc. 134 (2006), 3153-3157
MSC (2000): Primary 46A55; Secondary 26A21
DOI: https://doi.org/10.1090/S0002-9939-06-08683-7
Published electronically: June 5, 2006
MathSciNet review: 2231897
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Abstract: Let $ X$ be a simplex and $ K$ a compact subset of the set of all extreme points of $ X$. We show that any bounded function $ f$ of Baire class $ \alpha$ on $ K$ can be extended to a function $ h$ of affine class $ \alpha$ on $ X$. Moreover, $ h$ can be chosen in such a way that $ h(X)\subset \overline{\operatorname{co}} \,f(K)$.


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Additional Information

Jirí Spurny
Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: spurny@karlin.mff.cuni.cz

DOI: https://doi.org/10.1090/S0002-9939-06-08683-7
Keywords: Simplex, weak Dirichlet problem, affine functions, Baire functions
Received by editor(s): January 25, 2005
Published electronically: June 5, 2006
Additional Notes: The author is currently a Postdoctoral Fellow at the Department of Mathematical and Statistical Sciences of the University of Alberta, Edmonton. He would like to thank this department and, in particular, Prof. N. Tomczak–Jaegermann and Prof. V. Zizler for support and excellent working conditions.
This research was supported in part by the grants GAČR 201/03/0935, GAČR 201/03/D120, NSERC 7926, and in part by the Research Project MSM 0021620839 from the Czech Ministry of Education.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society