In mathematical analysis and in probability theory, a s-algebra (also sigma-algebra, s-field, sigma-field) on a set X is a collection S of subsets of X that is closed under countable-fold set operations (complement, union of countably many sets and intersection of countably many sets). By contrast, an algebra is only required to be closed under finitely many set operations. That is, a s-algebra is an algebra of sets, completed to include countably infinite operations. The pair (X, S) is also a field of sets, called a measurable space.