About: Schröder–Bernstein theorem for measurable spaces

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The Cantor–Bernstein–Schroeder theorem of set theory has a counterpart for measurable spaces, sometimes called the Borel Schroeder–Bernstein theorem, since measurable spaces are also called Borel spaces. This theorem, whose proof is quite easy, is instrumental when proving that two measurable spaces are isomorphic. The general theory of standard Borel spaces contains very strong results about isomorphic measurable spaces, see Kuratowski's theorem. However, (a) the latter theorem is very difficult to prove, (b) the former theorem is satisfactory in many important cases (see Examples), and (c) the former theorem is used in the proof of the latter theorem.

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rdfs:label	Schröder–Bernstein theorem for measurable spaces (en)
rdfs:comment	The Cantor–Bernstein–Schroeder theorem of set theory has a counterpart for measurable spaces, sometimes called the Borel Schroeder–Bernstein theorem, since measurable spaces are also called Borel spaces. This theorem, whose proof is quite easy, is instrumental when proving that two measurable spaces are isomorphic. The general theory of standard Borel spaces contains very strong results about isomorphic measurable spaces, see Kuratowski's theorem. However, (a) the latter theorem is very difficult to prove, (b) the former theorem is satisfactory in many important cases (see Examples), and (c) the former theorem is used in the proof of the latter theorem. (en)
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Link from a Wikipage to another Wikipage	Homeomorphic Cantor–Bernstein–Schroeder theorem Theorems in measure theory Measurable function Measurable space Descriptive set theory Topological spaces Theorems in the foundations of mathematics Closed interval Bijection Borel set Open interval Set theory Standard Borel space Schröder–Bernstein property Image (mathematics) Preimage
sameAs	Schröder–Bernstein theorem for measurable spaces Schröder–Bernstein theorem for measurable spaces Schröder–Bernstein theorem for measurable spaces
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has abstract	The Cantor–Bernstein–Schroeder theorem of set theory has a counterpart for measurable spaces, sometimes called the Borel Schroeder–Bernstein theorem, since measurable spaces are also called Borel spaces. This theorem, whose proof is quite easy, is instrumental when proving that two measurable spaces are isomorphic. The general theory of standard Borel spaces contains very strong results about isomorphic measurable spaces, see Kuratowski's theorem. However, (a) the latter theorem is very difficult to prove, (b) the former theorem is satisfactory in many important cases (see Examples), and (c) the former theorem is used in the proof of the latter theorem. (en)
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is Link from a Wikipage to another Wikipage of	Schroder-Bernstein theorem for measurable spaces Schröder–Bernstein theorem Ernst Schröder (mathematician) Schroeder–Bernstein theorem for measurable spaces Schröder–Bernstein Schröder–Bernstein property Schröder–Bernstein theorems for operator algebras Schroder–Bernstein theorem for measurable spaces Schroeder-Bernstein theorem for measurable spaces Schröder-Bernstein theorem for measurable spaces
is Wikipage redirect of	Schroder-Bernstein theorem for measurable spaces Schroeder–Bernstein theorem for measurable spaces Schroder–Bernstein theorem for measurable spaces Schroeder-Bernstein theorem for measurable spaces Schröder-Bernstein theorem for measurable spaces
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