This is an announcement for the paper "Perimeter under multiple Steiner symmetrizations" by Almut Burchard and Gregory R. Chambers. Abstract: Steiner symmetrization along n linearly independent directions transforms every compact subset of R^n into a set of finite perimeter. Archive classification: math.MG math.FA Mathematics Subject Classification: 28A75 (26B15, 52A38) Remarks: 12 pages, 1 figure Submitted from: almut@math.toronto.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.4521 or http://arXiv.org/abs/1209.4521