2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159189We prove that the martingale dimensions for canonical diffusion processes on a class of self-similar sets including nested fractals are always one. This provides an affirmative answer to the conjecture of S. Kusuoka [Publ. Res. Inst. Math. Sci. 25 (1989) 659--680].22 pages, 1 figureProbability60J60; 28A80; 31C25; 60G44text