Sweeping at the Martin boundary of a fine domain

TL;DR

This paper investigates the concept of sweeping on subsets of the Riesz-Martin space of a fine domain in Euclidean space, demonstrating the equivalence of sweeping notions under different topologies.

Contribution

It establishes the equivalence of sweeping with respect to the natural and minimal-fine topologies on subsets of the Riesz-Martin space of a fine domain.

Findings

Sweeping notions are identical under both topologies.

The study extends the understanding of potential theory in fine domains.

Results contribute to the theory of boundary behavior in potential theory.

Abstract

We study sweeping on a subset of the Riesz-Martin space of a fine domain in $\RR^n$ ($n\ge2$), both with respect to the natural topology and the minimal-fine topology, and show that the two notions of sweeping are identical.