A solution of the abstract Dirichlet problem for Baire-one functions (Q820061)

Let \(X\) be a nonempty compact convex subset of a locally convex space and let \(\text{ext}(X)\) stand for the extreme boundary of \(X\). Then each Baire-one function on \(\text{ext}(X)\) extends to an affine Baire-one function on \(X\) iff \(X\) is a Choquet simplex and \(\text{ext}(X)\) is a Lindelöf \(H\)-set in the Kuratowski sense.