Date of Award

1-1-2012

Language

English

Document Type

Master's Thesis

Degree Name

Master of Arts (MA)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (v, 37 pages) : illustrations.

Dissertation/Thesis Chair

Rongwei Yang

Committee Members

Kehe Zhu, Karin Reinhold, Rongwei Yang

Keywords

Banach-Tarski paradox, Measure theory, Decomposition (Mathematics), Cantor sets

Subject Categories

Physical Sciences and Mathematics

Abstract

Developed and published in the 1920s, Stefan Banach and Alfred Tarski gave a construction of a "paradoxical decomposition" of the unit sphere S2 that is now known to mathematicians as the Banach-Tarski Paradox. This paper explores how this paradox may be applied on the middle-third Cantor set C. This will require delving into the realms of mathematical analysis, measure and integration theory, probability theory, and even on the theory of free groups. The reader is assumed to have some basic knowledge in these mathematical subfields. Finally, the question of whether nonmeasurable sets exist in reality will be discussed.

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