The Banach-Tarski Paradox

Joel H. Shapiro
Lecture Notes, October 2014
Abstract: Notes for lectures I gave at the Portland State University Analysis Seminar during the Fall term 2014. The notes paradoxical decompositions, with special emphasis on the famous Banach-Tarski Theorem, which asserts that the unit ball of Euclidean 3-space can be partitioned into finitely many pieces which can be re-assembled, using only rigid transformations (i.e. isometries of R^3) into two copies of the unit ball.

Download .pdf file (680 KB)