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The Banach-Tarski Paradox

Stan Wagon
Publisher: 
Cambridge University Press
Publication Date: 
1993
Number of Pages: 
348
Format: 
Hardcover
Edition: 
2
Series: 
Encyclopedia of Mathematics and its Applications 163
Price: 
110.00
ISBN: 
9781107042599
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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.

Dummy View - NOT TO BE DELETED