A Ramsey theorem for measurable sets

Laczkovich, M.

doi:10.1090/S0002-9939-02-06403-1

A Ramsey theorem for measurable sets
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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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