This is an announcement for the paper "On the Yao-Yao partition theorem" by Joseph Lehec. Abstract: The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the space into 2^n regions of equal measure in such a way that every affine hyperplane avoids at least one of the regions. We give a constructive proof of this result and extend it to slightly more general measures. Archive classification: math.FA math.CO Mathematics Subject Classification: 52C99 Citation: Arch. Math. 92 (4) (2009) 366-376 Remarks: 10 pages, file might be slightly different from the published version Submitted from: lehec@ceremade.dauphine.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.2123 or http://arXiv.org/abs/1011.2123