  The notion of "super convex spaces" generalizes the idea of convex spaces by
replacing finite affine sums with countable affine sums. Using this notion
permits a very elegant approach for analysis of the Giry monad on standard
measurable spaces and identifying the $\mathcal{G}$-algebras for that monad. We
use Isbell duality and restrict the adjunction $\mathbf{Spec} \dashv
\mathcal{O}$ to a proper subcategory of super convex spaces and separated
standard measurable spaces.
