A structural characterization of numéraires of convex sets of nonnegative random variables

We introduce the concept of numéraire s of convex sets in L0+L+0 , the nonnegative orthant of the topological vector space L0 of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set C⊆L0+C⊆L+0 to be a numéraire of CC is given, inspired from ideas in financial mathematics.