On the Yao-Yao partition theorem
Résumé
The Yao-Yao partition theorem states that for any probability measure µ on R n having a density which is continuous and bounded away from 0, it is possible to partition R n into 2 n regions of equal measure for µ in such a way that every affine hyperplane of R n avoids at least one of the regions. We give a constructive proof of this result and extend it to slightly more general measures.
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