This is an announcement for the paper "A concentration inequality for product spaces" by Pandelis Dodos, Vassilis Kanellopoulos and Konstantinos Tyros. Abstract: We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior. Archive classification: math.PR math.CO math.FA Remarks: 11 pages, no figures Submitted from: pdodos@math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5965 or http://arXiv.org/abs/1410.5965