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In mathematical analysis and in probability theory,
a sigma-algebra (also sigma-field) on a set X
is a collection Sigma of subsets of X that includes X itself,
is closed under complement, and is closed under countable unions.

The definition implies that it also includes the empty subset and
that it is closed under countable intersections.

The pair (X, Sigma) is called a measurable space or Borel space.

A sigma-algebra is a type of algebra of sets.
An algebra of sets needs only to be closed under the union or
intersection of finitely many subsets,
which is a weaker condition.[1]

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