A mass partition problem in $\Bbb R^4$

Abstract

The paper considers the existence of the maximal possible hyperplanepartition of a continuous probability Borel measure in $\Bbb{R}^{4}$. Theemphases is on the use of the equivariant ideal valued index theory ofFadell and Husseini. The presented result is the tightest positive solutionto one of the oldest and most relentless partition problems posed by B. Grünbaum~[12].