Banach-Tarski paradox using pieces with the property of Baire.

@article{Dougherty1992BanachTarskiPU,
  title={Banach-Tarski paradox using pieces with the property of Baire.},
  author={R. Dougherty and M. Foreman},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1992},
  volume={89 22},
  pages={
          10726-8
        }
}
  • R. Dougherty, M. Foreman
  • Published 1992
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
In 1924 Banach and Tarski, using ideas of Hausdorff, proved that there is a partition of the unit sphere S2 into sets A1,...,Ak,B1,..., Bl and a collection of isometries [sigma1,..., sigmak, rho1,..., rhol] so that [sigma1A1,..., sigmakAk] and [rho1B1,..., rholBl] both are partitions of S2. The sets in these partitions are constructed by using the axiom of choice and cannot all be Lebesgue measurable. In this note we solve a problem of Marczewski from 1930 by showing that there is a partition… Expand
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