The Banach-Tarski paradox /
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 u...
| Autor principal: | |
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| Formato: | Libro |
| Lenguaje: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1993.
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| Edición: | 1st pbk. ed. |
| Materias: | |
| Acceso en línea: | Publisher description Table of contents |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
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| 049 | |a U@SA | ||
| 050 | 0 | 0 | |a QA248 |b .W25 1993 |
| 082 | 0 | 0 | |a 511.3/22 |2 20 |
| 100 | 1 | |a Wagon, S. | |
| 245 | 1 | 4 | |a The Banach-Tarski paradox / |c Stan Wagon. |
| 250 | |a 1st pbk. ed. | ||
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1993. | ||
| 300 | |a xviii, 253 p. : |b ill. ; |c 24 cm. | ||
| 504 | |a Includes bibliographical references (p. 236-248) and index. | ||
| 505 | 0 | |a 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 -- Appendix A, B, C -- Addendum to 2nd printing. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Banach-Tarski paradox. | |
| 650 | 0 | |a Measure theory. | |
| 650 | 0 | |a Decomposition (Mathematics) | |
| 650 | 7 | |a Paradoja de Banach-Tarski. |2 UDESA | |
| 650 | 7 | |a Medida, Teoría de la. |2 UDESA | |
| 650 | 7 | |a Descomposición (Matemáticas) |2 UDESA | |
| 856 | 4 | 2 | |3 Publisher description |u http://catdir.loc.gov/catdir/description/cam026/93246292.html |
| 856 | 4 | 1 | |3 Table of contents |u http://catdir.loc.gov/catdir/toc/cam028/93246292.html |