Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 231 - 241
Remarks on non-diagonality conditions for Sierpinski carpets
We prove the equivalence of three different formulations of non-diagonality for Sierpinski carpets given by Barlow, Bass, Kumagai and Teplyaev , by Hino  and by Kigami . 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.
Received: 15 January 2009
Revised: 11 June 2009
First available in Project Euclid: 24 November 2018
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Kajino, Naotaka. Remarks on non-diagonality conditions for Sierpinski carpets. Probabilistic Approach to Geometry, 231--241, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710231. https://projecteuclid.org/euclid.aspm/1543086321