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Statements

Subject Item: dbr:Schroder-Bernstein_theorem_for_measurable_spaces
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
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Subject Item: dbr:Schröder–Bernstein_theorem
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces

Subject Item: dbr:Ernst_Schröder_(mathematician)
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces

Subject Item: dbr:Schroeder–Bernstein_theorem_for_measurable_spaces
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
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Subject Item: dbr:Schröder–Bernstein
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
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Subject Item: dbr:Schröder–Bernstein_property
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces

Subject Item: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
rdf:type: yago:Abstraction100002137 yago:Theorem106752293 yago:Proposition106750804 yago:Message106598915 yago:Communication100033020 yago:WikicatTheoremsInMeasureTheory yago:Statement106722453 yago:WikicatTheoremsInTheFoundationsOfMathematics
rdfs:label: Schröder–Bernstein theorem for measurable spaces
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.
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dbo: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.
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foaf:isPrimaryTopicOf: wikipedia-en:Schröder–Bernstein_theorem_for_measurable_spaces

Subject Item: dbr:Schröder–Bernstein_theorems_for_operator_algebras
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces

Subject Item: dbr:Schroder–Bernstein_theorem_for_measurable_spaces
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
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Subject Item: dbr:Schroeder-Bernstein_theorem_for_measurable_spaces
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
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Subject Item: dbr:Schröder-Bernstein_theorem_for_measurable_spaces
dbo:wikiPageWikiLink: dbr:Schröder–Bernstein_theorem_for_measurable_spaces
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Subject Item: wikipedia-en:Schröder–Bernstein_theorem_for_measurable_spaces
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