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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.

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    $\begingroup$ I suppose you would like the measures to be non-atomic? $\endgroup$ – Anthony Quas Mar 13 '18 at 5:09
  • $\begingroup$ @AnthonyQuas Yes $\endgroup$ – Ma Joad Mar 13 '18 at 6:14
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    $\begingroup$ Why are you editing your own post to replace a period with a non-standard little circle? Avoid useless edits. The only benefit of this one is that probably somebody will make the reverse edit at some point. If the goal is to reappear in the front list, it's a bit too visible. $\endgroup$ – YCor Mar 14 '18 at 13:12
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    $\begingroup$ Again, Avoid unnecessary edits. You've just again done 4 unnecessary edits to 4 of your questions. $\endgroup$ – YCor Mar 17 '18 at 7:50
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The 7-day-old paper by Alfredo Hubard answers this question positively.

Update on 16 May: The paper has been revised. It is now coauthored with Roman Karasev and claims to treat only the case when the dimension is of the form $2^t$.

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    $\begingroup$ Remark 9 in v2 explains the error in the first version. $\endgroup$ – j.c. May 16 '18 at 17:50

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