Minimal fine limits on trees
type: Item
instance of: scholarly article
title: Minimal fine limits on trees
zbMATH Open document ID: 1067.31004
author: Kohur Gowrisankaran
author: David Singman
published in: Illinois Journal of Mathematics
publication date: 2005-02-25T00:00:00Z
review text: The authors define the minimal filter corresponding to each boundary point of a tree and prove a tree version of the Fatou-Naim-Doob limit theorem. Also, it is given an example of a tree for which minimal fine limits do not imply nontangential limits, even for positive superharmonic functions. Motivated by work on potential theory on halfspaces and Brelot spaces, it is defined the harmonic fine filter corresponding to each boundary point of the tree. In contrast to the classical setting the harmonic fine filter is the same as the minimal fine filter.
reviewed by: Sophia L. Kalpazidou
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 31C40
zbMATH DE Number: 2138863
zbMATH Keywords: minimal fine limits on tree
zbMATH Keywords: Fatou-Naim-Doob limit theorem
zbMATH Keywords: harmonic fine filter
zbMATH Keywords: minimal fine filter
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2138863