Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.
@article{bwmeta1.element.doi-10_2478_BF02476543, author = {Ji\v r\'\i\ Spurn\'y}, title = {The Dirichlet problem for Baire-one functions}, journal = {Open Mathematics}, volume = {2}, year = {2004}, pages = {260-271}, zbl = {1072.46011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02476543} }
Jiří Spurný. The Dirichlet problem for Baire-one functions. Open Mathematics, Tome 2 (2004) pp. 260-271. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02476543/
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