  In this note, we discuss the concept of pseudoeffective vector bundle and
also introduce pseudoeffective torsion-free sheaves over compact K\"ahler
manifolds. We show that a pseudoeffective reflexive sheaf over a compact
K\"ahler manifold with vanishing first Chern class is in fact a numerically
flat vector bundle. A proof is obtained through a natural construction of
positive currents representing the Segre classes of pseudoeffective vector
bundles.
