Lusin'S Separation Theorem

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What is Lusin's separation 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 = ∅. It is named after Nikolai Luzin, who proved it in 1927. The theorem can be generalized to show that for each sequence (An) of disjoint analytic sets there is a sequence (Bn) of disjoint Borel sets such that An ⊆ Bn for each n. An immediate consequence is Suslin's theorem, which states that if a set and its complement are both analytic, then the set is Borel.

Technology Types

descriptive set theorypropositionstatementtheoremtheorems in the foundations of mathematictheorems in topologytheory

Synonyms

Lusin separation theorem

Translations

Luzins separationssats (sv)

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