Division point measures resulting from triangle subdivisions
type: Item
instance of: scholarly article
title: Division point measures resulting from triangle subdivisions
zbMATH Open document ID: 1248.28003
author: Jeanette Olli
published in: Geometriae Dedicata
publication date: 2012-06-26T00:00:00Z
review text: If the unit interval \([0,1]\) is divided into \([0,\alpha]\) and \([\alpha,1]\) and then subdivided iteratively in the same proportions, then it is well-known that the weak*-limit measure of the uniform measure on the division points is mutually singular to Lebesgue if \(\alpha\neq\frac12\). \textit{S. Kakutani} [Lect. Notes Math. 541, 369--375 (1976; Zbl 0363.60023)] showed that dividing at each stage only those intervals of greatest length in the same proportions gives convergence to Lebesgue measure for any \(\alpha\in(0,1)\). Here natural analogues of these results are found for certain division schemes of a right triangle.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 6050463
zbMATH Keywords: division scheme
zbMATH Keywords: equidistribution
MaRDI profile type: Publication
full work available at URL: s10711-011-9621-0
OpenAlex ID: W2030967515
cites work: Uniform distribution of Kakutani's interval splitting procedure
cites work: Ergodic theory on compact spaces
cites work: Symmetric Measures on Cartesian Products
cites work: Conjugacies for tiling dynamical systems
cites work: Generalized Hewitt-Savage Theorems for Strictly Stationary Processes
cites work: An Introduction to Symbolic Dynamics and Coding
cites work: A singular random measure generated by splitting [0, 1]
cites work: Weak convergence results for the Kakutani interval splitting procedure.
cites work: Symmetry of tilings of the plane
cites work: The pinwheel tilings of the plane
cites work: Space tilings and substitutions
cites work: Some generalizations of the pinwheel tiling
DOI: 10.1007/S10711-011-9621-0
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description: scientific article; zbMATH DE number 6050463