Given $nD$ finite measures $µ_1, . . ., µ_{nD}$ in $\mathbb{R}^n$ does there exists a set of at most D hyperplanes that bisect each of the measures?

How far is this problem explained?

That is closely related to a conjecture in *L. Barba and P. Schnider, Sharing a pizza: bisecting masses with two cuts, Proceedings of the 29th Canadian
Conference on Computational Geometry, CCCG’17*.

Definition: A Hyperplane bisects $\mu$ iff the value of $\mu$ on two sides of the hyperplane are equal.

Avoid unnecessary edits. You've just again done 4 unnecessary edits to 4 of your questions. $\endgroup$ – YCor Mar 17 '18 at 7:50