“Lusin's separation theorem”的意思、由来-开放百科全书

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Lusin's separation theorem

释义

Notes
References

{{otheruses4|the separation theorem|the theorem on continuous functions|Lusin's theorem}}

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 = ∅.^[1] It is named after Nikolai Luzin, who proved it in 1927.^[2]

The theorem can be generalized to show that for each sequence (A_n) of disjoint analytic sets there is a sequence (B_n) of disjoint Borel sets such that A_n ⊆ B_n for each n. ^[1]

An immediate consequence is Suslin's theorem, which states that if a set and its complement are both analytic, then the set is Borel.

Notes

1. ^¹{{harv|Kechris|1995|p=87}}.
2. ^{{harv|Lusin|1927}}.

References

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3 : Descriptive set theory|Theorems in the foundations of mathematics|Theorems in topology

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