> Borel means that it includes all finite open intervals in the real numbers. So (0,1) but not [0,1]. The Borel algebra is generated by open sets, but it inclu

> Borel means that it includes all finite open intervals in the real numbers. So (0,1) but not [0,1]. The Borel algebra is generated by open sets, but it includes complements (and therefore closed sets) as well. In fact it's also generated by closed sets. The Borel algebra of R also contains sets like the rationals and the irrationals. The types of sets that aren't included in the Borel algebra (but are in the Lebesgue) are nasty things like (some) subsets of the cantor set.