Dissertations and Theses @ UNI
Availability
Open Access Thesis
Keywords
Minkowski geometry; Generalized spaces;
Abstract
In this work we investigate the behavior of the Minkowski Functionals admitted by a sequence of sets which converge to the unit ball ‘from the inside’. We begin in R 2 and use this example to build intuition as we extend to the more general R n case. We prove, in the penultimate chapter, that convergence ‘from the inside’ in this setting is equivalent to two other characterizations of the convergence: a geometric characterization which has to do with the sizes of the faces of each polytope in the sequence converging to zero, and the convergence of the Minkowski functionals defined on the approximating sets to the Euclidean Norm. In the last chapter we explore how we can extend our results to infinite dimensional vector spaces by changing our definition of polytope in that setting, the outlook is bleak.
Year of Submission
2016
Degree Name
Master of Arts
Department
Department of Mathematics
First Advisor
Douglas Musapiri, Chair
Date Original
5-2016
Object Description
1 PDF file (vii, 28 pages)
Copyright
©2016 Jesse Moeller
Language
en
File Format
application/pdf
Recommended Citation
Moeller, Jesse, "Some convergence properties of Minkowski functionals given by polytopes" (2016). Dissertations and Theses @ UNI. 244.
https://scholarworks.uni.edu/etd/244
