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A Ramsey theorem for measurable sets


Author: M. Laczkovich
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
Published electronically: March 13, 2002
MathSciNet review: 1908933
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Abstract | References | Similar Articles | Additional Information

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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  • M. L. Brodskii, On some properties of sets of positive measure (Russian), Uspekhi Mat. Nauk. 4, No. 3, 31 (1949), 136-139.
  • Z. Buczolich, Product sets in the plane, sets of the form $A+B$ on the real line and Hausdorff measures, Acta Math. Hungar. 65 (1994), no. 2, 107–113. MR 1278763, DOI https://doi.org/10.1007/BF01874307
  • H. G. Eggleston, Two measure properties of Cartesian product sets, Quart. J. Math. Oxford (2) 5 (1954), 108-115.
  • F. Galvin, Partition theorems for the real line, Notices Amer. Math. Soc. 15 (1968), 660.
  • F. Galvin, Errata to “Partition theorems for the real line”, Notices Amer. Math. Soc. 16 (1969), 1095.
  • Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597
  • Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578

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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.
Article copyright: © Copyright 2002 American Mathematical Society