  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 $\tilde{P}$.
Importantly, we do not restrict our analysis to balanced MVPSs, in the
terminology of $k$-color urns, but rather show that the only non-balanced
exchangeable MVPSs are sequences of i.i.d. random variables.
