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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The use of shears to construct paradoxes in $\textbf {R}^{2}$
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by Stanley Wagon PDF
Proc. Amer. Math. Soc. 85 (1982), 353-359 Request permission

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.
References
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 353-359
  • MSC: Primary 28C10; Secondary 51M99
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0656101-5
  • MathSciNet review: 656101