Let 𝑋 be some set, and let 𝑃(𝑋) represent its power set. Then a subset 𝐹⊆𝑃(𝑋) is called a σ-algebra if it satisfies the following three properties:
𝐹 contains 𝑋: 𝑋∊𝐹
𝐹 is closed under complements: if 𝐴∊𝐹, then also 𝑋\𝐴∊𝐹
𝐹 is closed under countable unions: if 𝐴𝑖∊ 𝐹 for 𝑖=1,2,…, then also (⋃1≤𝑖≤∞ 𝐴𝑖) ∊ 𝐹
𝐹 is closed under countable intersections: if 𝐴𝑖∊ 𝐹 for 𝑖=1,2,…, then also (⋂1≤𝑖≤∞ 𝐴𝑖) ∊ 𝐹 # the corollary from the previous two properties and De Morgan’s law