Key points are not available for this paper at this time.
Christoph Bandt, Siegfried Graf, Self-Similar Sets 7. A Characterization of Self-Similar Fractals with Positive Hausdorff Measure, Proceedings of the American Mathematical Society, Vol. 114, No. 4 (Apr., 1992), pp. 995-1001
Bandt et al. (Wed,) studied this question.