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.
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Digital Object Identifier: 10.2969/aspm/05710231