Continuity of relative entropy of entanglement

We show that an entanglement measure called relative entropy of entanglemen t satisfies a strong continuity condition. If two states are close to each other then so are their entanglements per particle pair in this measure. It follows in particular, that the measure is appropriate for the description of entanglement manipulations in the limit of an infinite number of pairs of particles. (C) 1999 Published by Elsevier Science B.V. All rights reserv ed.