Suppose $X$ is a set and $M$ is a σ-algebra of subsets of $X$.

A σ-ideal of $M$ is a subset $N\subset M$ that is closed under countable unions and passage to subsets: if $a\in N$, $b\in M$, and $b\subset a$, then $b\in N$.

Sometimes we do not have a canonical measure $\mu$ at our disposal, but we do have a canonical σ-ideal of negligible sets. This is the case, for example, for smooth manifolds and locally compact groups.