In mathematics, a σ-algebra (or sigma-algebra) (sigma is a Greek letter, upper case Σ, lower case σ) over a set X is a nonempty collection Σ of subsets of X that is close under complementation and countable unions of its members. It is a Boolean algebra, completed to include countably infinite operations. The pair <X, Σ> is also a field of sets, sometimes called a σ-field or a measurable space.