What Are Sigma Algebras?

In mathematical analysis and in probability theory, a σ-algebra on a set X: is a collection \Sigma of subsets of X including X itself, it is closed under complement, it is closed under countable unions, it includes the empty subset, and it is closed under countable intersections.

What exactly is a sigma-algebra?

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

What are sigma algebras used for?

Sigma algebra is necessary in order for us to be able to consider subsets of the real numbers of actual events. In other words, the sets need to be well defined, under the conditions of countable unions and countable intersections, for it to have probabilities assigned to it.