Sigma-algebra

This page is under construction.

A $\sigma$-algebra is an algebra that is closed under countable unions. Thus a $\sigma$-algebra is a nonempty collection A of subsets of a nonempty set X closed under countable unions and complements.

Examples of $\sigma$-algebras

• Given a set $X$, then $2^{X}$ and $\{\emptyset ,X\}$ are $\sigma$-algebras.