Abstract
Let B1,B2,…,Bm be nonempty finite subsets of Rd with Bi not contained in an affine hyperplane for each i∈{2,3,…,m}. In this paper we find a nontrivial lower bound of |B1+B2+…+Bm|. As a consequence of this result, a problem by M. Matolcsi and I. Z. Ruzsa is also solved.
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