Definition 22.4.1 (Scaffold*).label Let $(X, \cm, \mu)$ be a measure space and $\cf \subset \bracs{A \in \cm|\mu(A) < \infty}$ be an ideal, then $\cf$ is a scaffold for $\mu$ if for all $E \in \cm$,

and the quadruple $(X, \cm, \cf, \mu)$ is a scaffolded measure space.

For any semifinite measure space $(X, \cm, \mu)$, $\cf = \bracs{A \in \cm|\mu(A) < \infty}$ is the canonical scaffold for $\mu$, and $(X, \cm, \mu)$ will be equipped with this scaffold unless specified otherwise.