2024/01/31 by M. C. Crabb, Crabb, M. C.
Mathematics · #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2403.08794
We give a direct proof of a result due to Karasev (2008), Karasev-Matschke (2014) and Schnider-Soberón (2023). Given m+1 Borel probability measures on the space of affine hyperplanes in a real vector space V of dimension m+1, there exist a line L through the origin in V and a point v∈ L such that at least half of the hyperplanes, as counted by any of the measures, meet or are parallel to each of the two closed rays in L meeting at v.