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Date of Award
Master of Science (MS)
Gardner, Richard J.
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.
Minkowski geometry, Set theory, Convex domains, Convex bodies
Western Washington University
Copying of this thesis in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this thesis for commercial purposes, or for financial gain, shall not be allowed without the author's written permission.
Mesikepp, Tim, "M-addition" (2013). WWU Graduate School Collection. 275.