This is an announcement for the paper "A characterization of the Radon-Nikodym property" by Robert Deville and Oscar Madiedo. Abstract: It is well known that every bounded below and non increasing sequence in the real line converges. We give a version of this result valid in Banach spaces with the Radon-Nikodym property, thus extending a former result of A. Proch\'azka. Archive classification: math.FA Mathematics Subject Classification: 91A05, 46B20, 46B22 Remarks: 10 pages, 2 figures Submitted from: oscar.reynaldo@mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.1721 or http://arXiv.org/abs/1303.1721