This is an announcement for the paper "On the von Bahr--Esseen inequality" by Iosif Pinelis. Abstract: The well-known von Bahr--Esseen bound on the absolute pth moments of martingales with p in (1,2] is extended to a large class of moment functions, and now with a best possible constant factor (which depends on the moment function). As an application, measure concentration inequalities for separately Lipschitz functions on product spaces are obtained. Relations with p-uniformly smooth and q-uniformly convex normed spaces are discussed. Archive classification: math.PR math.FA Mathematics Subject Classification: Primary 60E15, 60B11, 62G10, secondary 46B09, 46B20, 46B10 Submitted from: ipinelis@mtu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1008.5350 or http://arXiv.org/abs/1008.5350