On the Yao-Yao partition theorem

TL;DR

This paper provides a constructive proof of the Yao-Yao partition theorem, demonstrating how to partition a measure with a continuous, bounded density into regions avoiding hyperplanes, and extends the theorem to more general measures.

Contribution

It offers a constructive proof of the Yao-Yao partition theorem and extends its applicability to broader classes of measures.

Findings

Constructive proof of the Yao-Yao partition theorem

Extension to more general measures with continuous, bounded densities

Partitioning into 2^n regions of equal measure avoiding hyperplanes

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.