The tangent measure distribution of self-conformal fractals
type: Item
instance of: scholarly article
title: The tangent measure distribution of self-conformal fractals
zbMATH Open document ID: 1089.28007
author: Norbert Patzschke
published in: Monatshefte für Mathematik
publication date: 2004-12-16T00:00:00Z
review text: The tangent measure distributions of a fractal measure \(\mu\) at a point \(x\) of its support are random measures which reflect, loosely speaking, the scaled structure of \(\mu\) seen by an observer zooming into \(x\). They were first introduced in an unpublished work of Bandt, see \textit{S. Graf} [Monatsh. Math. 120, No.~3--4, 223--246 (1995; Zbl 0841.28011)], though crucial ideas were already present in the seminal work of \textit{U. Zähle} [Probab. Theory Relat. Fields 80, No.1, 79--100 (1988; Zbl 0638.60064)]. In the present paper tangent measure distributions of self-conformal fractals are investigated. It is shown that for this class of fractal measures there is a unique tangent measure distribution at \(\mu\)-almost every point \(x\), and, moreover, this tangent measure distribution is independent of \(x\).
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 2123206
zbMATH Keywords: tangent measures
zbMATH Keywords: random fractals
zbMATH Keywords: open set condition
MaRDI profile type: Publication
full work available at URL: s00605-004-0253-4
OpenAlex ID: W2009442475
DOI: 10.1007/S00605-004-0253-4
description: scientific article; zbMATH DE number 2123206