  We prove a strong maximum principle for Schr\"odinger operators defined on a
class of fractal sets and their blowups without boundary. Our primary interest
is in weaker regularity conditions than have previously appeared in the
literature; in particular we permit both the fractal Laplacian and the
potential to be Radon measures on the fractal. As a consequence of our results,
we establish a Harnack inequality for solutions of these operators.
