The Banach–Tarski Paradox, 2nd ed. (Encyclopedia of Mathematics and Its Applications, Vol. 163) '16
Wagon, Stan, Tomkowicz, Grzegorz 著
内容
目次
Part I. Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures: 1. Introduction; 2. The Hausdorff paradox; 3. The Banach-Tarski paradox: duplicating spheres and balls; 4. Hyperbolic paradoxes; 5. Locally commutative actions: minimizing the number of pieces in a paradoxical decomposition; 6. Higher dimensions; 7. Free groups of large rank: getting a continuum of spheres from one; 8. Paradoxes in low dimensions; 9. Squaring the circle; 10. The semigroup of equidecomposability types; Part II: Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions: 11. Transition; 12. Measures in groups; 13. Applications of amenability; 14. Growth conditions in groups and supramenability; 15. The role of the axiom of choice.
