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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
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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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

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