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Author:   Stan Wagon
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   24
ISBN:  

9780511609596

ISBN 10:   0511609590
Publication Date:   05 August 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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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.

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

' ... 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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