Sigma-Algebra

Definition

A $\sigma$-algebra in a set $X$ is a collection of subsets, so called measurable sets, of $X$ such that (the requirements are):

1. $X\in M$
2. $A\in M⟹A^{\complement }\in M$ ($X^{\complement }=\varnothing \in M$)
3. $A_n\in M⟹{\cup }_{n=1}^{\infty }{A}_n\in M$ ($⟹{\cap }_{n=1}^{\infty }{A}_n=({\cup }_{n=1}^{\infty }{A}^{\complement }{)}^{\complement }\in M)$)

Related Terminologies/Functions

• Measurable
• Measure