Theorem

minimal postulates for a σ\sigma-field 𝒜\mathcal{A}

  1. Ω∈𝒜\Omega \in \mathcal{A}
  2. A∈𝒜⟹A∁∈𝒜A \in \mathcal{A} \implies A^{\complement} \in \mathcal{A}
  3. Ai∈𝒜,i=1,2,⋯⟹∪Ai∈𝒜A_i \in \mathcal{A}, i = 1, 2, \dots \implies \cup A_i \in \mathcal{A}