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.
Recommended Citation
Munshi, Sachin, "The Banach-Tarski paradox on the middle-third cantor set C" (2012). Legacy Theses & Dissertations (2009 - 2024). 713.
https://scholarsarchive.library.albany.edu/legacy-etd/713