Injective positively ordered monoids I

AbstractWe define a certain notion of completeness for a wide class of commutative (pre)ordered monoids (from now on P.O.M.'s). This class seems to be the natural context for studying structures like measurable functions spaces, equidecomposability types of spaces, partially ordered abelian groups and cardinal algebras. Then, we can prove that roughly speaking, spaces of measures with values in complete P.O.M.'s are complete P.O.M.'s. Furthermore, this notion of completeness yields us an ‘arithmetical’ characterization of injective P.O.M.'s