Sweeping at the Martin Boundary of a Fine Domain

We study sweeping on a subset of the Riesz-Martin space of a fine domain in ℝn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{n}$\end{document} (n≥2), both with respect to the natural topology and the minimal-fine topology, and show that the two notions of sweeping are identical.