A note on the boundary behavior for non-negative finely superharmonic functions in the upper half space (Q1191048)

The following result is proved: Let \(U\) be finely open in the upper half space \(H\subset\mathbb{R}^ d\), \(d\geq 2\), let \(\Delta_ 1(U)=\{\zeta\in\partial H\mid H\backslash U\) minimally thin at \(\zeta\}\), and let \(u\geq 0\) be finely superharmonic in \(U\). Then, at a.e. \(\zeta\in\Delta_ 1(U)\), there exists a polar set \(N(\zeta)\subset B(\zeta,1)\) such that the radial limit satisfies \(\lim_{U\ni z\to\zeta}u(z)=\allowbreak\hbox{}f\)-lim