目次

Part I. Paradoxical Decompositions, or the Nonexistence of FinitelyAdditive Measures: 1. Introduction; 2. The Hausdorff Paradox; 3. TheBanach Tarski Paradox: duplication spheres and balls; 4. Locallycommutative actions: minimizing the number of pieces in a paradoxicaldecomposition; 5. Higher dimensions and non-Euclidean spaces; 6. Freegroups of large rank: getting a continuum of spheres from one; 7.Paradoxes in low dimensions; 8. The semi-group of equideomposabilitytypes; Part II. Finitely Additive Measures, or the Nonexistence ofParadoxical 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 ofthe axiom of choice.