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The Banach-Tarski paradox Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland, Stan Wagon, Macalester College, St. Paul, Minnesota

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Author(s): Tomkowicz, Grzegorz; Wagon, Stan
Series: Encyclopedia of mathematics and its applications 163
Edition: Second edition
Publisher: Cambridge University Press
Year: 2016

Language: English
Pages: 348
Tags: Banach-Tarski paradox.;Measure theory.;Decomposition (Mathematics);Banach-Tarski paradox;Measure theory

Content: 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.