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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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A Ramsey theorem for measurable sets
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by M. Laczkovich PDF
Proc. Amer. Math. Soc. 130 (2002), 3085-3089 Request permission

Abstract:

We prove that if $X$ is a perfect Polish space and $[X]^2 =P_0 \cup \ldots \cup P_{k-1}$ is a partition with universally measurable pieces, then there is Cantor set $C\subset X$ with $[C]^2 \subset P_i$ for some $i.$
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Additional Information
  • M. Laczkovich
  • Affiliation: Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétàny 1/C, 1117 Hungary – and – Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England
  • Email: laczko@renyi.hu
  • Received by editor(s): February 2, 2000
  • Received by editor(s) in revised form: May 17, 2001
  • Published electronically: March 13, 2002
  • Communicated by: Carl G. Jockusch, Jr.
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 3085-3089
  • MSC (2000): Primary 03E02, 28A05
  • DOI: https://doi.org/10.1090/S0002-9939-02-06403-1
  • MathSciNet review: 1908933