  A. Sannami constructed an example of the differentiable Cantor set embedded
in the real line whose difference set has a positive measure. In this paper, we
generalize the definition of the difference sets for sets of the two
dimensional Euclidean space as the sets of vectors between two sets, and
estimate their measures. For the quadratic map Q_c(z)=z^2+c, we obtain that the
measure of the difference set of its Julia set vanishes if |c|>3+sqrt{3}.
