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We investigate the class of unital C*-algebras that admit a unital embeddinginto every unital C*-algebra of real rank zero, that has no finite-dimensionalquotients. We refer to a C*-algebra in this class as an initial object. We showthat there are many initial objects, including for example some unital, simple,infinite-dimensional AF-algebras, the Jiang-Su algebra, and the GICAR-algebra.  That the GICAR-algebra is an initial object follows from an analysis ofHausdorff moment sequences. It is shown that a dense set of Hausdorff momentsequences belong to a given dense subgroup of the real numbers, and hence thatthe Hausdorff moment problem can be solved (in a non-trivial way) when themoments are required to belong to an arbitrary simple dimension group (i.e.,unperforated simple ordered group with the Riesz decomposition property).

Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C*-Algebras of Real Rank Zero