Hausdorff convergence of Julia sets

Consider a sequence {g(d)}(d is an element of N) converging uniformly on compact sets to g, where g and g(d) are meromorphic functions on C. We show that the Julia sets J(g(d)) converge to the Julia set J(g) in the Hausdorff metric, if the Fatou set F(g) is the union of basins of attracting periodic orbits and infinity is an element of J(g). This result is discussed for families of finite type depending on a parameter, which is illustrated with the polynomials lambda(1 + 2/d)(d) converging to lambda e(z).