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M-Addition, Tim Mesikepp
M-Addition, Tim Mesikepp
WWU Graduate School Collection
This study builds upon the work of Gardner, Hug and Weil [1, Section 6] by further exploring the properties of M-addition. It is shown that several well-known theorems on Minkowski addition have M-addition parallels, including results involving intersections, the valuation property and the convex hull. The last of these enables us to detail su cient conditions for when the M-sum of convex polytopes is a convex polytope. Nested operations of M-addition are also examined and an M-addition generalization of the Shapley-Folkman Lemma and a related bound are offered.