Joel H. Shapiro
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.
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