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The Banach-Tarski Paradox
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Details

  • Page extent: 272 pages
  • Size: 234 x 156 mm
  • Weight: 0.45 kg

Library of Congress

  • Dewey number: 511.3/22
  • Dewey version: 20
  • LC Classification: QA248 .W22 1993
  • LC Subject headings:
    • Banach-Tarski paradox
    • Measure theory
    • Decomposition (Mathematics)

Library of Congress Record

Paperback

 (ISBN-13: 9780521457040 | ISBN-10: 0521457041)

  • There was also a Hardback of this title but it is no longer available | Adobe eBook
  • Published September 1993

Replaced by 9781107617315

$57.00 (P)

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.

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.

Reviews

"...a readable and stimulating book." Ward Henson, American Scientist

"...packed with fascinating and beautiful results." R.J. Gardner, Bulletin of the London Mathematical Society

"...this beautiful book is written with care and is certainly worth reading." Wlodzimierz Bzyl, Mathematical Reviews

'In 1985 Stan Wagon wrote The Banach-Tarski Paradox, which not only became the classic text on paradoxical mathematics, but also provided vast new areas for research. The new second edition, co-written with Grzegorz Tomkowicz, a Polish mathematician who specializes in paradoxical decompositions, exceeds any possible expectation I might have had for expanding a book I already deeply treasured. The meticulous research of the original volume is still there, but much new research has also been included.' John J. Watkins, MAA Reviews

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