A type of Strassen's Theorem for measures taking values in the positive cone of a Banach lattice is proved. We generalize a result of A. Hirshberg and R. M. Shortt and formulate a type of Strassen's Theorem in a topological context via closed sets.
"On the Existence of Vector Measures with Given Marginals." Real Anal. Exchange 25 (1) 437 - 448, 1999/2000.