Definition:Null Set/Signed Measure

Definition

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

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

Let $N \in \Sigma$.

We say that $N$ is a $\mu$-null set if and only if:

for each $A \in \Sigma$ with $A \subseteq N$, we have $\map \mu A = 0$