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I'm trying to find a proof that any two uncountable Borel subsets of a Polish space are Borel isomorphic. I've been trying to find it in Kechris' "Classical Descriptive Set Theory" but I've been having difficulty finding it. If anyone knew a reference that would be great.

Rupert
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1 Answers1

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Donald L. Cohn, Measure Theory (Birkhäuser 1980) First Edition

Theorem 8.3.6, page 275 (2nd Edition, p. 259)

alternate proof: Exercise 5, page 277. Outline:
(a) Every Borel subset of a Polish space is Borel isomorphic to a Borel subset of $\{0,1\}^{\mathbf N}$.
(b) Each uncountable Borel subset of a Polish space has a Borel subset that is Borel isomorphic to $\{0,1\}^{\mathbf N}$.
(c) a Borel version of Cantor-Bernstein

GEdgar
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