Definition 6

— Let $A$ be a $\mu$-measurable subset of $X$. A set $\mathscr{K}$ of compact subsets of $A$ is said to be $\mu$-dense in $A$ if it satisfies the conditions (PLI), (PLII), $a), b), c), d)$ of Prop. 12.

The set of all compact subsets of $A$ is $\mu$-dense in $A$.

When $A = X$, we shall say simply ' $\mu$-dense set' in place of 'set $\mu$-dense in $X$'. If $X - A$ is locally $\mu$-negligible, then every set of compact subsets of $A$ that is $\mu$-dense in $A$ is also $\mu$-dense in $X$.