Sigma-algebra

A Sigma-algebra of sets, or $\sigma$-algebra is very similar to a $\sigma$-ring of sets.

Like how ring of sets and algebra of sets differ, the same applies to $\sigma$-ring compared to $\sigma$-algebra

Definition

A non empty class of sets $S$ is a $\sigma$-algebra if

• if $$A\in S$$ then $$A^c\in S$$
• if $$\{A_n\}_{n=1}^\infty\subset S$$ then $$\cup^\infty_{n=1}A_n\in S$$

That is it is closed under complement and countable union