Representations of pseudo Vitali spaces and Loomis-Sikorski Theorem

We present pseudo Vitali spaces as lattices with a partially defined operation,+ , that is not necessarily commutative. We show that they can be embedded into l-groups, and we give a categorical equivalence of the category of pseudo Vitali spaces. Studying states on Vitali spaces with strong unit, we show that every Dedekind sigma-complete Vitali space is an epimorphic image of a Vitali space of bounded functions where the operations on functions are defined pointwise.