... that (1, 0, 1) ≈ (0, 1, 7), (0, 7, 0, 1) ≈ (1, 1, 7, 7) and (1, a, 0, 1) ≈ (0, a, 7, 7) for any a ∈ D We call each element in the set { (1, 0, 1), (0, 1, 7), (0, 7, 0, 1), (1, 1, 7, 7), (1, a, ... = (1, 0, 1, , 1, 0, 1, ) or x = (1, 1, 0, 1, , 1, 0, 1, ) ∞ or x = (1, 1, 1, 0, 1, , 1, 0, 1, ) ∈ D∞ and s = i=1 3−i xi ∈ supp µ, we have √ log(1 + 3) α(s) = − log Proof The ... dimensions of fractal probability measures associated with equal probability weight, Preprint T Hu, N Nguyen and T Wang, Local dimensions of the probability measure associated with the (0, 1, 3) - problem, ...