Abstract
We prove the equivalence of three different formulations of non-diagonality for Sierpinski carpets given by Barlow, Bass, Kumagai and Teplyaev [5], by Hino [10] and by Kigami [12]. We also derive some geometric property of Sierpinski carpets from the non-diagonality. As an application, we give a simpler treatment of a criterion stated in Kigami [12, Section 3.4] for the volume doubling property of self-similar measures on Sierpinski carpets.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1202.28010
MathSciNet: MR2648262
Digital Object Identifier: 10.2969/aspm/05710231
Subjects:
Primary:
28A80
,
31C25
,
60J45
Keywords:
Generalized Sierpinski carpet
,
non-diagonality
,
Self-similar measure
,
volume doubling property
Rights: Copyright © 2010 Mathematical Society of Japan
