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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The weak Dirichlet problem for Baire functions
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by Jiří Spurný PDF
Proc. Amer. Math. Soc. 134 (2006), 3153-3157 Request permission


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
  • Jiří Spurný
  • Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
  • Email:
  • 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 GA ČR 201/03/0935, GA ČR 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
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3153-3157
  • MSC (2000): Primary 46A55; Secondary 26A21
  • DOI:
  • MathSciNet review: 2231897