The Banach-Tarski Paradox / Edition 1

The Banach-Tarski Paradox / Edition 1

by Stan Wagon
     
 

ISBN-10: 0521457041

ISBN-13: 9780521457040

Pub. Date: 09/28/1993

Publisher: Cambridge University Press

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.  See more details below

Overview

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.

Product Details

ISBN-13:
9780521457040
Publisher:
Cambridge University Press
Publication date:
09/28/1993
Series:
Encyclopedia of Mathematics and its Applications Series, #24
Edition description:
New Edition
Pages:
272
Sales rank:
1,188,245
Product dimensions:
6.14(w) x 9.21(h) x 0.63(d)

Table of Contents

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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