# Category:Sigma-Algebras

This category contains results about Sigma-Algebras.
Definitions specific to this category can be found in Definitions/Sigma-Algebras.

Let $X$ be a set.

A $\sigma$-algebra $\Sigma$ over $X$ is a system of subsets of $X$ with the following properties:

 $(\text {SA} 1)$ $:$ Unit: $\ds X \in \Sigma$ $(\text {SA} 2)$ $:$ Closure under Complement: $\ds \forall A \in \Sigma:$ $\ds \relcomp X A \in \Sigma$ $(\text {SA} 3)$ $:$ Closure under Countable Unions: $\ds \forall A_n \in \Sigma: n = 1, 2, \ldots:$ $\ds \bigcup_{n \mathop = 1}^\infty A_n \in \Sigma$

## Subcategories

This category has the following 7 subcategories, out of 7 total.