An algebra is a family $R$ of subsets of a set $X$ s.t.:

• $\emptyset \in R$
• Closed under finite unions. $A,B \in R \Rightarrow A \cup B \in R$
• Closed under complements. $A \in R \Rightarrow X \setminus A \in R$

If the algebra is closed under countable unions (not just finite), then it is a Sigma-algebra

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