The Banach-Tarski paradox
著者
書誌事項
The Banach-Tarski paradox
Cambridge University Press, 1993
1st pbk. ed
- : pbk
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注記
Includes bibliographical references (p. 236-248) and index
内容説明・目次
内容説明
The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up-to-date proofs and discusses many unsolved problems.
目次
- 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 equideomposability 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.
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