Dixmier always solves this as follows, e.g. in *C\*-algebras* — surely *one possible example* of good exposition (E. C. Lance’s translator‘s preface: “With is clear and straightforward style, this remains the best book form which to learn about *C\**-algebras”):

>**16.1. The compact group associated with a topological group**

>**16.1.1. Theorem.** *Let $G$ be a topological group. There exists a compact
group $\Sigma$ and a continuous morphism $\alpha:G\to\Sigma$ possessing the following property: for every compact group $\Sigma'$ and every continuous morphism $\alpha':G\to\Sigma'$, there exists a unique continuous morphism $\beta:\Sigma\to\Sigma'$ such that $\alpha'= \beta\circ\alpha$. Furthermore, the pair $(\Sigma,\alpha)$ is determined up to isomorphism by this property.*

>(... Long proof goes here ...)

>**16.1.2. Definition.** The group $\Sigma$ is called the *compact group associated
with* $G$, and $\alpha$ is called the *canonical morphism of $G$ into $\Sigma$*.

The book has about two dozen “X.Y.2” definitions like this — e.g. no less than six over pp. 116–123 (disjoint representations, factor representation, quasi-equivalent representations, type I, multiplicity-free, multiplicity), and the almost last statement in the book is a definition (Plancherel measure). Of course, this is not the only way — contrast an epigraph in Reed & Simon, *Functional Analysis*:

> *A good definition should be the hypothesis of a theorem. (J. Glimm)*