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A sigma-algebra on a set $\Omega$ is a collection $\mathcal{F}$ of subsets of $\Omega$ that satisfies three specific closure properties: it must contain the whole space $\Omega$, it must be closed under complements, and it must be closed under countable unions.

Conditions: $\Omega$ is a set.; $\mathcal{F}$ is a collection of subsets of $\Omega$.

A sigma-algebra on a set $\Omega$ is a collection $\mathcal{F}$ of subsets of $\Omega$ that satisfies three specific closure properties: it must contain the whole space $\Omega$, it must be closed under complements, and it must be closed under countable unions.

Conditions: $\Omega$ is a set.; $\mathcal{F}$ is a collection of subsets of $\Omega$.