A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable unions and intersections. Formally, the class B of Borel sets in Euclidean R^n is the smallest collection of sets that includes the open and closed sets such that if E, E_1, E_2, ... are in B, then so are union _(i = 1)^∞ E_i, intersection _(i = 1)^∞ E_i, and R^n \E, where F\E is a set difference . The set of rational numbers is a Borel set, as is the Cantor set.
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