TY - BOOK ID - 16460684 TI - The Banach-Tarski paradox PY - 1985 VL - v. 24 SN - 0521302447 9780521302449 PB - Cambridge: Cambridge university press, DB - UniCat KW - Banach-Tarski paradox KW - Measure theory KW - Decomposition (Mathematics) KW - Banach-Tarski paradox. KW - Decomposition (Mathematics). KW - Measure theory. KW - Lebesgue measure KW - Measurable sets KW - Measure of a set KW - Algebraic topology KW - Integrals, Generalized KW - Measure algebras KW - Rings (Algebra) KW - Mathematics KW - Probabilities KW - Paradox, Banach-Tarski KW - Axiom of choice KW - Sphere KW - Décomposition (Mathématiques) KW - Mesure, Théorie de la UR - https://www.unicat.be/uniCat?func=search&query=sysid:16460684 AB - The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. 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. ER -