Dama: up to L-spaces and the proof (completed up to properties of the
absolute value) that every complete integration riesz space is an L-space.
Now the plan is to prove the Lebesgue dominated convergence theorem for
L-spaces as Fremlin does and to build a model of them later on as suggested
by Spitters. Note: the proof of the theorem by Spitters is almost trivial
because it really exploits the fact the L0 is the (Cauchy) completion of L1.
The proof by Fremlin is much more general since it does not assume anything
more on L-spaces.
Note: we could also prove that every L-space is archimedean.