Banach–Tarski paradox (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Banach–Tarski paradox" in English language version.

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Olivier, Leroy (1995). Théorie de la mesure dans les lieux réguliers. ou : Les intersections cachées dans le paradoxe de Banach-Tarski (Report). arXiv:1303.5631.

arxiv.org

Olivier, Leroy (1995). Théorie de la mesure dans les lieux réguliers. ou : Les intersections cachées dans le paradoxe de Banach-Tarski (Report). arXiv:1303.5631.
Simon, Robert; Tomkowicz, Grzegorz (2024). "A measure theoretic paradox from a continuous colouring rule". Math. Ann. 389 (2): 1441–1462. arXiv:2203.11158. doi:10.1007/s00208-023-02644-4.

doi.org

Wilson, Trevor M. (September 2005). "A continuous movement version of the Banach–Tarski paradox: A solution to De Groot's problem". Journal of Symbolic Logic. 70 (3): 946–952. CiteSeerX 10.1.1.502.6600. doi:10.2178/jsl/1122038921. JSTOR 27588401. S2CID 15825008.
Simpson, Alex (1 November 2012). "Measure, randomness and sublocales". Annals of Pure and Applied Logic. 163 (11): 1642–1659. doi:10.1016/j.apal.2011.12.014. hdl:20.500.11820/47f5df74-8a53-452a-88c0-d5489ee5d659.
Banach, Stefan; Tarski, Alfred (1924). "Sur la décomposition des ensembles de points en parties respectivement congruentes" (PDF). Fundamenta Mathematicae (in French). 6: 244–277. doi:10.4064/fm-6-1-244-277.
Robinson, Raphael M. (1947). "On the Decomposition of Spheres". Fund. Math. 34: 246–260. doi:10.4064/fm-34-1-246-260. This article, based on an analysis of the Hausdorff paradox, settled a question put forth by von Neumann in 1929:
Foreman, M.; Wehrung, F. (1991). "The Hahn–Banach theorem implies the existence of a non-Lebesgue measurable set" (PDF). Fundamenta Mathematicae. 138: 13–19. doi:10.4064/fm-138-1-13-19.
Pawlikowski, Janusz (1991). "The Hahn–Banach theorem implies the Banach–Tarski paradox" (PDF). Fundamenta Mathematicae. 138: 21–22. doi:10.4064/fm-138-1-21-22.
Churkin, V. A. (2010). "A continuous version of the Hausdorff–Banach–Tarski paradox". Algebra and Logic. 49 (1): 81–89. doi:10.1007/s10469-010-9080-y. S2CID 122711859. Full text in Russian is available from the Mathnet.ru page.
On p. 85. Neumann, J. v. (1929). "Zur allgemeinen Theorie des Masses" (PDF). Fundamenta Mathematicae. 13: 73–116. doi:10.4064/fm-13-1-73-116.
Satô, Kenzi (2003). "A locally commutative free group acting on the plane". Fundamenta Mathematicae. 180 (1): 25–34. doi:10.4064/fm180-1-3.
Tomkowicz, Grzegorz (2011). "A free group of piecewise linear transformations". Colloquium Mathematicum. 125 (2): 141–146. doi:10.4064/cm125-2-1.
Adams, John Frank (1954). "On decompositions of the sphere". J. London Math. Soc. 29: 96–99. doi:10.1112/jlms/s1-29.1.96.
Mycielski, Jan (1955). "On the paradox of the sphere". Fund. Math. 42 (2): 348–355. doi:10.4064/fm-42-2-348-355.
Tomkowicz, Grzegorz (2017). "On decompositions of the hyperbolic plane satisfying many congruences". Bulletin of the London Mathematical Society. 49: 133–140. doi:10.1112/blms.12024. S2CID 125603157.
Mycielski, Jan (1989). "The Banach-Tarski paradox for the hyperbolic plane". Fund. Math. 132 (2): 143–149. doi:10.4064/fm-132-2-143-149.
Mycielski, Jan; Tomkowicz, Grzegorz (2013). "The Banach-Tarski paradox for the hyperbolic plane (II)". Fund. Math. 222 (3): 289–290. doi:10.4064/fm222-3-5.
Tomkowicz, Grzegorz (2017). "Banach-Tarski paradox in some complete manifolds". Proc. Amer. Math. Soc. 145 (12): 5359–5362. doi:10.1090/proc/13657.
Tomkowicz, Grzegorz (2018). "A properly discontinuous free group of affine transformations". Geom. Dedicata. 197: 91–95. doi:10.1007/s10711-018-0320-y. S2CID 126151042.
Mycielski, Jan; Tomkowicz, Grzegorz (2019). "On the equivalence of sets of equal measures by countable decomposition". Bulletin of the London Mathematical Society. 51: 961–966. doi:10.1112/blms.12289. S2CID 209936338.
Simon, Robert; Tomkowicz, Grzegorz (2024). "A measure theoretic paradox from a continuous colouring rule". Math. Ann. 389 (2): 1441–1462. arXiv:2203.11158. doi:10.1007/s00208-023-02644-4.
Tomkowicz, Grzegorz (2024). "On bounded paradoxical sets and Lie groups". Geom. Dedicata. 218 (3) 72. doi:10.1007/s10711-024-00923-1.

eudml.org

Robinson, Raphael M. (1947). "On the Decomposition of Spheres". Fund. Math. 34: 246–260. doi:10.4064/fm-34-1-246-260. This article, based on an analysis of the Hausdorff paradox, settled a question put forth by von Neumann in 1929:

files.wordpress.com

terrytao.files.wordpress.com

Tao, Terence (2011). An introduction to measure theory (PDF). p. 3. Archived from the original (PDF) on 6 May 2021.

handle.net

hdl.handle.net

Simpson, Alex (1 November 2012). "Measure, randomness and sublocales". Annals of Pure and Applied Logic. 163 (11): 1642–1659. doi:10.1016/j.apal.2011.12.014. hdl:20.500.11820/47f5df74-8a53-452a-88c0-d5489ee5d659.

icm.edu.pl

matwbn.icm.edu.pl

Banach, Stefan; Tarski, Alfred (1924). "Sur la décomposition des ensembles de points en parties respectivement congruentes" (PDF). Fundamenta Mathematicae (in French). 6: 244–277. doi:10.4064/fm-6-1-244-277.
Foreman, M.; Wehrung, F. (1991). "The Hahn–Banach theorem implies the existence of a non-Lebesgue measurable set" (PDF). Fundamenta Mathematicae. 138: 13–19. doi:10.4064/fm-138-1-13-19.
Pawlikowski, Janusz (1991). "The Hahn–Banach theorem implies the Banach–Tarski paradox" (PDF). Fundamenta Mathematicae. 138: 21–22. doi:10.4064/fm-138-1-21-22.
On p. 85. Neumann, J. v. (1929). "Zur allgemeinen Theorie des Masses" (PDF). Fundamenta Mathematicae. 13: 73–116. doi:10.4064/fm-13-1-73-116.

jstor.org

Wilson, Trevor M. (September 2005). "A continuous movement version of the Banach–Tarski paradox: A solution to De Groot's problem". Journal of Symbolic Logic. 70 (3): 946–952. CiteSeerX 10.1.1.502.6600. doi:10.2178/jsl/1122038921. JSTOR 27588401. S2CID 15825008.

mathnet.ru

Churkin, V. A. (2010). "A continuous version of the Hausdorff–Banach–Tarski paradox". Algebra and Logic. 49 (1): 81–89. doi:10.1007/s10469-010-9080-y. S2CID 122711859. Full text in Russian is available from the Mathnet.ru page.

psu.edu

citeseerx.ist.psu.edu

Wilson, Trevor M. (September 2005). "A continuous movement version of the Banach–Tarski paradox: A solution to De Groot's problem". Journal of Symbolic Logic. 70 (3): 946–952. CiteSeerX 10.1.1.502.6600. doi:10.2178/jsl/1122038921. JSTOR 27588401. S2CID 15825008.

semanticscholar.org

api.semanticscholar.org

Wilson, Trevor M. (September 2005). "A continuous movement version of the Banach–Tarski paradox: A solution to De Groot's problem". Journal of Symbolic Logic. 70 (3): 946–952. CiteSeerX 10.1.1.502.6600. doi:10.2178/jsl/1122038921. JSTOR 27588401. S2CID 15825008.
Churkin, V. A. (2010). "A continuous version of the Hausdorff–Banach–Tarski paradox". Algebra and Logic. 49 (1): 81–89. doi:10.1007/s10469-010-9080-y. S2CID 122711859. Full text in Russian is available from the Mathnet.ru page.
Tomkowicz, Grzegorz (2017). "On decompositions of the hyperbolic plane satisfying many congruences". Bulletin of the London Mathematical Society. 49: 133–140. doi:10.1112/blms.12024. S2CID 125603157.
Tomkowicz, Grzegorz (2018). "A properly discontinuous free group of affine transformations". Geom. Dedicata. 197: 91–95. doi:10.1007/s10711-018-0320-y. S2CID 126151042.
Mycielski, Jan; Tomkowicz, Grzegorz (2019). "On the equivalence of sets of equal measures by countable decomposition". Bulletin of the London Mathematical Society. 51: 961–966. doi:10.1112/blms.12289. S2CID 209936338.

web.archive.org

Tao, Terence (2011). An introduction to measure theory (PDF). p. 3. Archived from the original (PDF) on 6 May 2021.