This is an announcement for the paper "Equimeasurabily and isometries in noncommutative Lp-spaces" by Mikael de la Salle. Abstract: We prove some noncommutative analogues of a theorem by Rudin and Plotkin about equimeasurability and isometries in L_p-spaces. Let 0<p<\infty, p not an even integer. The main result of this paper states that in the category of unital subspaces of noncommutative probability Lp-spaces, the unital completely isometric maps come from *-isomorphisms of the underlying von Neumann algebras. Unfortunately we are only able to treat the case of bounded operators. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L53; 46L51; 47L05 Remarks: 11 pages The source file(s), article_arxiv.bbl: 2056 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0707.0427 or http://arXiv.org/abs/0707.0427 or by email in unzipped form by transmitting an empty message with subject line uget 0707.0427 or in gzipped form by using subject line get 0707.0427 to: math@arXiv.org.