ENGLISH

The Banach-Tarski paradox Grzegorz Tomkowicz, Centrum Edukacji G2, Bytom, Poland, Stan Wagon, Macalester College, St. Paul, Minnesota

By Stan , Tomkowicz , Grzegorz; Wagon

Book information

Publisher
Cambridge University Press
Year
2016
ISBN
978-1-107-04259-9, 1107042593
Language
english
Format
PDF
Filesize
5 MB (5503766 bytes)
Series
Encyclopedia of mathematics and its applications 163
Edition
Second edition
Pages
348\366
Topic
Mathematics Logic
Library
kolxo3
Time added
2019-04-25 18:00:00
Banach-Tarski paradox.;Measure theory.;Decompositi

Description

Content: 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.

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