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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 $\Omega$.

A path from the root records the ordered partial sequence of chosen jobs. Following a route in the drawn tree corresponds to selecting the jobs along that route in order; for example, the route using $J_1$ then $J_4$ means doing job 1 and job 4 and not taking jobs 2 and 3 along that partial path.

Conditions: The tree is the job-sequencing state-space tree drawn on the board.; Each edge label indicates appending one job to the current partial sequence.

A path from the root records the ordered partial sequence of chosen jobs. Following a route in the drawn tree corresponds to selecting the jobs along that route in order; for example, the route using $J_1$ then $J_4$ means doing job 1 and job 4 and not taking jobs 2 and 3 along that partial path.

Conditions: The tree is the job-sequencing state-space tree drawn on the board.; Each edge label indicates appending one job to the current partial sequence.