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{{about|the separation theorem|the theorem on continuous functions|Lusin's theorem}} |
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In [[descriptive set theory]] and [[mathematical logic]], '''Lusin's separation theorem''' states that if ''A'' and ''B'' are disjoint [[Analytic set|analytic subsets]] of [[Polish space]], then there is a [[Borel set]] ''C'' in the space such that ''A'' |
In [[descriptive set theory]] and [[mathematical logic]], '''Lusin's separation theorem''' states that if ''A'' and ''B'' are disjoint [[Analytic set|analytic subsets]] of [[Polish space]], then there is a [[Borel set]] ''C'' in the space such that ''A'' ⊆ ''C'' and ''B'' ∩ ''C'' = ∅ (Kechris 1995, p. 87). It is named after [[Nicolas Lusin]], who proved it in 1927. |
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== References == |
== References == |
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*{{ cite book |
*{{ cite book |
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| author = Alexander Kechris |
| author = Alexander Kechris |
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| authorlink = Alexander S. Kechris |
| authorlink = Alexander S. Kechris |
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[[Category:Theorems in the foundations of mathematics]] |
[[Category:Theorems in the foundations of mathematics]] |
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[[Category:Theorems in topology]] |
[[Category:Theorems in topology]] |
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Revision as of 03:53, 12 November 2011
In descriptive set theory and mathematical logic, Lusin's separation theorem states that if A and B are disjoint analytic subsets of Polish space, then there is a Borel set C in the space such that A ⊆ C and B ∩ C = ∅ (Kechris 1995, p. 87). It is named after Nicolas Lusin, who proved it in 1927.
References
- Alexander Kechris (1995). Classical descriptive set theory. Graduate texts in mathematics. Vol. 156. ISBN 0-387-943734-9.
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value: length (help) - Nicolas Lusin (1927). "Sur les ensembles analytiques" (PDF). Fundamenta Mathematicae (in French). 10: 1–95.