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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The use of shears to construct paradoxes in $ {\bf R}\sp{2}$


Author: Stanley Wagon
Journal: Proc. Amer. Math. Soc. 85 (1982), 353-359
MSC: Primary 28C10; Secondary 51M99
MathSciNet review: 656101
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Abstract: It is shown that the addition of a certain shear transformation to the planar isometry group is sufficient to allow a Banach-Tarski type paradox to be constructed in $ {{\mathbf{R}}^2}$. This paradox is then combined with a result of Rosenblatt to obtain a characterization of two-dimensional Lebesgue measure as a finitely additive measure.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0656101-5
PII: S 0002-9939(1982)0656101-5
Keywords: Paradoxes, finitely additive measures
Article copyright: © Copyright 1982 American Mathematical Society