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
of Borel sets in Euclidean 
is the smallest collection of sets that includes the open
and closed sets such that if 
,
, 
, ... are in 
, then so are 
, 
, and 
, where 
is a set difference (Croft
et al. 1991).
The set of rational numbers is a Borel set, as is the Cantor set.
