  We investigate the Eilenberg-Moore algebras for the Giry monad defined on the
category of measurable spaces using super convex spaces. The category of super
convex spaces has a subcategory consisting of the one point extension of the
real line, and the truncated Yoneda embedding arising from the full subcategory
with that one object is full, although it is not faithful. By restricting to
those super convex spaces which are coseparable by the one point extension of
the real line, the truncated Yoneda embedding is full and faithful. This
permits the construction of a barycenter map used to factorize the Giry monad,
and obtain an equivalence of categories.
