Seemingly completely forgotten, back in 1936, the Dutch mathematician Freudenthal, quite well known at the time, proved his so called Spectral Theorem, see chapter 6 in Luxemburg & Zaanen : Riesz Spaces I. North-Holland, 1971. The amusing thing is that the theorem is formulated eclusively in terms of partial orders, and on top of it, its proof is also in the very same terms. Yet one of the rather direct consequences of it is the spectral representation of normal operators in Hilbert spaces. Another one is the Radon-Nykodim theorem in measure theory. And to aggravate things, it can also solve some Poisson PDEs.
Does anybody know about more recent applications of that theorem ? And how about having more appreciation for the concept of partial order ?