\(Q\)-compactification of harmonic spaces and the Choquet simplex (Q1860771)

Let \(X\) be a harmonic space, and let \(X^*\) be an arbitrary metrizable and resolutive compactification of \(X\). Extending an idea of \textit{P. A. Loeb} [Isr. J. Math. 25, 154-187 (1976; Zbl 0346.31007)], the authors construct for \(X^*\) a compactification \(\widehat{X}\) that enables simplicial considerations. In the case where every bounded harmonic function is obtained by the PWB method, \(\widehat{X}\) is just Loeb's compactification.