On the set of regular boundary points
type: Item
instance of: scholarly article
title: On the set of regular boundary points
zbMATH Open document ID: 0546.31006
author: Kirsti Oja
published in: Osaka Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: It is well known that for an open set in a Brelot harmonic space, the set \(U_{reg}\) of regular boundary points of U is dense in \(\partial\bar U\); but this is not valid for more general harmonic spaces. In this paper, the author considers a general P-harmonic space X with a countable base and proves the following result: If U is a Keldyš set (i.e., a relatively compact open set such that \(\partial U\backslash U_{reg}\) has vanishing harmonic measure at each point in U), or if X has a base of regular sets and U is any open set, then \(\bar U\backslash\overline{U_{reg}}\) is an absorbent set of \(X\backslash\overline{U_{reg}}\).
Mathematics Subject Classification ID: 31D05
zbMATH DE Number: 3869712
zbMATH Keywords: Brelot harmonic space
zbMATH Keywords: regular boundary points
zbMATH Keywords: P-harmonic space
reviewed by: Fumi-Yuki Maeda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3869712