The closedness of the free-disposal hull of a production set

Assume thatL is a topological vector lattice andY is a closed subset ofL + ×R N, whereR N denotes theN-dimensional Euclidean space. It is shown that the setY−L + ×R + N is closed ifY has appropriate monotonicity properties. The result is applicable to the case ofL equal toL ∞ with the Mackey topology, τ(L ∞,L 1).