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 â C and B ∩ C = â . It is named after Nikolai Luzin, who proved it in 1927.
The theorem can be generalized to show that for each sequence (A<sub>n</sub>) of disjoint analytic sets there is a sequence (B<sub>n</sub>) of disjoint Borel sets such that A<sub>n</sub> â B<sub>n</sub> 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.