On the decomposition of non-negative finely harmonic functions (Q1119778)

Let \(U\subset {\mathbb{R}}^ n\) be a fine domain and \(f\geq 0\) be a finely harmonic function in U. Defining quasi-bounded and singular finely harmonic functions in the usual way, the main theorem says that f admits a unique decomposition \(f=f_ 1+f_ 2\) into quasi-bounded and singular parts \(f_ 1\), \(f_ 2\). The theorem will be proved by a probabilistic approach.