The space L-W(1) (nu) of all scalarly integrable functions with respect to a Frechet-space-valued vector measure nu is shown to be a complete Frechet lattice with the sigma-Fatou property which contains the (traditional) space L-1 (nu), of all nu-integrable functions. Indeed, L-1 (nu) is the or-order continuous part of L-W(1) (nu). Every Frechet lattice with the sigma-Fatou property and containing a weak unit in its sigma-order continuous part is Frechet lattice isomorphic to a space of the kind L-W(1) (nu).