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)
sameAs	Schröder–Bernstein theorem for measurable spaces
dbp:wikiPageUsesTemplate	dbt:Color
Subject	Descriptive set theory Theorems in the foundations of mathematics Theorems in measure theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Schröder–Bernstein_theorem_for_measurable_spaces?oldid=818252032&ns=0
Wikipage page ID	18998319 (xsd:integer)
page length (characters) of wiki page	4314 (xsd:nonNegativeInteger)
Wikipage revision ID	818252032 (xsd:integer)
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)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Schröder–Bernstein_theorem_for_measurable_spaces
is Wikipage redirect of	Schroder-Bernstein theorem for measurable spaces Schroder–Bernstein theorem for measurable spaces Schroeder-Bernstein theorem for measurable spaces Schröder-Bernstein theorem for measurable spaces Schroeder–Bernstein theorem for measurable spaces
is Link from a Wikipage to another Wikipage of	List of theorems Ernst Schröder (mathematician)

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