Definition:Negligible Set

Definition

Let $\struct {X, \Sigma, \mu}$ be a measure space.

We say that a subset $N \subseteq X$ is $\mu$-negligible if and only if:

there exists $N' \in \Sigma$ with $N \subseteq N'$ such that $\map \mu {N'} = 0$.

Sources

• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $1.5$: Completeness and Regularity