Exact packing measure of linear Cantor sets

Let K be the attractor of a linear iterated function system S(j)x = rho(j)x+b(j) (j = 1,...,m) on the real line satisfying the open set condition (where the open set is an interval). It is well known that the packing dimension of K is equal to alpha, the unique positive solution y of the equation Sigma(j=1)(m) rho(j)(y) = 1; and the alpha-dimensional packing measure P-alpha(K) is finite and positive. Denote by y the unique self-similar measure for the IFS {S-j}(j=1)(m) with the probability weight {rho(j)(alpha)}(j=1)(m). In this paper, we prove that P-alpha(K) is equal to the reciprocal of the so-called "minimal centered density" of mu, and this yields an explicit formula of P-alpha(K) in terms of the parameters rho(j), b(j) (j = 1,...,m). Our result implies that P-alpha(K) depends continuously on the parameters whenever Sigma(j) rho(j) < 1.