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Measure-valued P\'olya urn sequences (MVPS) are a generalization of the
observation processes generated by $k$-color P\'olya urn models, where the
space of colors $\mathbb{X}$ is a complete separable metric space and the urn
composition is a finite measure on $\mathbb{X}$, in which case reinforcement
reduces to a summation of measures. In this paper, we prove a representation
theorem for the reinforcement measures $R$ of all exchangeable MVPSs, which
leads to a characterization result for their directing random measures
$\tilde{P}$. In particular, when $\mathbb{X}$ is countable or $R$ is dominated
by the initial distribution $\nu$, then any exchangeable MVPS is a Dirichlet
process mixture model over a family of probability distributions with disjoint
supports. Furthermore, for all exchangeable MVPSs, the predictive distributions
converge on a set of probability one in total variation to $\tilde{P}$. A final
result shows that $\tilde{P}$ can be decomposed into an absolutely continuous
and a mutually singular measure with respect to $\nu$, whose support is
universal and does not depend on the particular instance of $\tilde{P}$.