Type: Article

An extension of a theorem of Yao and Yao

Roldán-Pensado, Edgardo; Soberón, Pablo;

Abstract:

A theorem of Yao and Yao asserts that given an absolutely continuous probability measure on Rd, it is possible to find an equipartition (i.e., a partition whose parts have the same measure) of the space into at most 2d convex subsets such that every affine hyperplane avoids at least one of these subsets. The main result of this article is the existence of an equipartition into at most 3×2d?1 convex subsets such that every affine hyperplane avoids at least two of them. The authors also give an application to a problem of separation of points and hyperplanes.