No \(b\)-concentrated measures with \(b<1.01\)
type: Item
instance of: scholarly article
title: No \(b\)-concentrated measures with \(b<1.01\)
zbMATH Open document ID: 0810.28002
author: Zoltán Buczolich
published in: Real Analysis Exchange
publication date: 1995-04-02T00:00:00Z
review text: A locally finite Borel measure \(\mu\) on \(R\) (\(R\) -- the real line) is said to be \(b\)-concentrated at the point \(x\in \text{supp}(\mu)\) with a \(b> 0\) if \(\lim_{h\to 0+} \mu((x- bh, x+ bh))/\mu((x- h,x+ h))< b\) holds. Let \(C_ b(\mu)\) be the set of all points where \(\mu\) is \(b\)- concentrated. The measure is said to be \(b\)-concentrated if \(C_ b(\mu)= \text{supp}(\mu)\). The author proves that there is no continuous non-zero \(b\)-concentrated measure with \(b< 1.01\). (This improves some of known results of the paper of the author and \textit{M. Laczkovich} [Acta Math. Hung. 57, No. 3/4, 349- 362 (1991; Zbl 0752.28002)]).
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 28A15
Mathematics Subject Classification ID: 26A24
zbMATH DE Number: 627528
zbMATH Keywords: locally finite Borel measure
zbMATH Keywords: \(b\)-concentrated measure
reviewed by: Pavel Kostyrko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 627528