Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
Full-text PDF

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 $i.$


References [Enhancements On Off] (What's this?)

  • 1. M. L. Brodskii, On some properties of sets of positive measure (Russian), Uspekhi Mat. Nauk. 4, No. 3, 31 (1949), 136-139. MR 11:18a
  • 2. 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 95g:28016
  • 3. H. G. Eggleston, Two measure properties of Cartesian product sets, Quart. J. Math. Oxford (2) 5 (1954), 108-115. MR 16:344e
  • 4. F. Galvin, Partition theorems for the real line, Notices Amer. Math. Soc. 15 (1968), 660.
  • 5. F. Galvin, Errata to ``Partition theorems for the real line'', Notices Amer. Math. Soc. 16 (1969), 1095.
  • 6. A. S. Kechris: Classical Descriptive Set Theory. Graduate Texts in Mathematics No. 156. Springer, 1995. MR 96e:03057
  • 7. S. Saks: Theory of the Integral. Dover, 1965. MR 29:4850

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03E02, 28A05

Retrieve articles in all journals with MSC (2000): 03E02, 28A05


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

DOI: https://doi.org/10.1090/S0002-9939-02-06403-1
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

American Mathematical Society