Borel set [SEP] named after
Borel set
In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel.
For a topological space "X", the collection of all Borel sets on "X" forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on "X" is the smallest
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 ("A