2 problems

Soberón–Takahashi conjecture. Any $d+k-1$ finite absolutely continuous measures on $\mathbb{R}^d$ can be simultaneously bisected by the chessboard coloring induced by $k$ or fewer…

Let $d,k\geq 1$, and let a finite measure in $\mathds{R}^d$ be bisected by a chessboard coloring if the two color classes have equal measure. Takahashi–Soberón conjecture. For any…