On the pointwise densities of the Cantor measure

Let K(a) be the symmetrical Cantor set generated by ?₀(x)=ax and ?₁(x)=ax+(1−a), where 0<a<1/2. Let s be the Hausdorff dimension of K(a) and μ the Cantor measure. In this paper, under the hypothesis that a is slightly greater than 1/3, we obtain the explicit formulas of the upper and lower s-densities Θ?s(μ,x), for every point x∈K(a). Moreover, we describe the range of a key quantity τ(x) in these formulas.