Bibliographical references C. Bandt, Deterministic Fractals and Fractal Measures, Lecture Notes of the School on Measure Theory and Real Analysis, Grado, Italy, 1991. A.S. Besicovitch, On the Sum of Digits of Real Numbers Represented in the Dyadic System, Math. Annalen, 110 (1934), 321-30. P. BiIlingsley, Probability and Measure, Wiley, New York, 1978. G. Brown, G. Michon and J. Peyriere, On the Mulfifractal Analysis of Measures, J. Stat. Physics 66 (1992), 775-790. R. Cawley and R.D. Mauldin, Multifractal Decomposition of Moran Fractals, Adtl. in Math. 92 (1992), 196-236. C.D. Cutler, The HausdorffDimension Distribution ofFinite Measures in Euclidean Spaces, Canad. J. Math. (1986) 38 (6), 1459-1484. C.D. Cutler, Connecting Ergodicity and Dimension in Dynamical Systems, Ergodic Theory Dyn. Syst. (1990) 10 451-462. A. Deliu, J.S. Geronimo, R. Shonkwiler and D. Hardin, Dimensions Associated with Recurrent Self-similar Sets, Math. Proc. Camb. Phil. Soc. 110 (1991), 327-36. H.G. Egglestone, The Fractional Dimension of a Set Defined by Decimal Properties, Quart. J. of Math. Oxford Ser. 20 (1949), 31-6. K.J. Falconer, The Geometry 01 Fractal Sets, Cambridge University Press, 1985. H. Haase, Densities of Hausdorff Measures on Generalized Self-Similar Sets, preprint. J .E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 30 (1981), 713-47. R.D. Mauldin and M. Urbanski, Dimensions and Measures in Infinnite Iterated Function Systems, Proc. London Math. Soc.(to appear). M. Morán, Hausdorff Measure of Infinitely Generated Self-Similar Sets, Monast. fur Math. (forthcoming). M. Morán and J.-M. Rey, Singularity of Self-Similar Measures with respect to Hausdorff Measures, preprint. L. Olsen, A Multifractal Formalism, Adv. in Math. (to appear). J.-M. Rey, Geometría de Medidas y Conjuntos Autosemejantes, Ph.D. thesis, Universidad Complutense de Madrid, 1995. C.A. Rogers and S.J. Taylor, Functions Continuous and Singular with respect to a Hausdorff Measure, Mathematika, 8 (1961), 1-31. A. Schief, Separation Properties for Self-Similar Seta, Proc. Amer. Math. Soc. 122 (1994), 111-115. D.W. Spear, Measures and Self-Similarity, Adv. in Math. 91(2) (1992), 143-157. S.J. Taylor, The Measure Theory of Random Fractals, Math. Proc. Camb. Phil. Soc. 100 (1986),383-406. S.J. Taylor and C. Tricot, Packing Measure, and its Evaluation for a Brownian Path, Trans. Amer. Math. Soc. 288(2) (1985), 679-699. C. Tricot, Two Definitions ofFractional Dimension, Math. Proc. Camb. Phil. Soc. 91 (1982), 57-74. P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, 1982. K.R. Wicks, Fractals and Hyperspaces, Lecture Notes in Math. 1492, Springer-Verlag, 1992. L.-S. Young, Dimension, Entropy and Liapunov Exponents, Ergodic Theory & Dynamical Systems 2 (1982), 109-24.