O. Musin

Borsuk-Ulam type theorem for the orthogonal group and orthogonal four-partitions

Makeev [2] stated that every finite Borel measure in $\mathbb R^d$ assigning zero mass to hyperplanes can be cut by $d$ mutually orthogonal hyperplanes so that every pair divides the measure into four equal parts, and outlined a proof strategy, but the key steps were left incomplete. We give a direct and elementary pro...