# 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. $A \in M \implies A^{\complement} \in M$ ($X^{\complement} = \emptyset \in M$)
3. $A_{n} \in M \implies \cup^{\infty}_{n=1} A_{n} \in M$ ($\implies \cap^{\infty}_{n=1} A_{n} = (\cup^{\infty}_{n=1}A^{\complement})^{\complement} \in M)$)
# Related Terminologies/Functions
- [[Measurable]]
- [[Measure]]