Table of contents for The Banach-Tarski paradox / Stan Wagon.


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Part I. Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures: 1. Introduction
2. The Hausdorff paradox
3. The Banach-Tarski paradox: duplication spheres and balls
4. Locally commutative actions: minimizing the number of pieces in a paradoxical decomposition
5. Higher dimensions and non-Euclidean spaces
6. Free groups of large rank: getting a continuum of spheres from one
7. Paradoxes in low dimensions
8. The semi-group of equidemomposability types
Part II. Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions: 9. Transition
10. Measures in groups
11. Applications of amenability: Marczewski measures and exotic measures
12. Growth conditions in groups and supramenability
13. The role of the axiom of choice.