a1 Department of Mathematics, University College London, Gower Sreet, London WC1E 6BT, U.K. (email: firstname.lastname@example.org)
We prove the following generalization of the ham sandwich theorem, conjectured by Imre Bárány. Given a positive integer k and d nice measures μ1,μ2,…,μd in d such that μi(d)=k for all i, there is a partition of d into k interior-disjoint convex parts C1,C2,…,Ck such that μi (Cj)=1 for all i,j. If k=2 , this gives the ham sandwich theorem. This result was proved independently by R. N. Karasev.
(Received October 29 2010)
(Online publication October 21 2011)