Definition:Negative Set

Definition

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

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

Let $A \in \Sigma$.

We say that $A$ is a $\mu$-negative set if and only if:

for each $E \in \Sigma$ with $E \subseteq A$ we have $\map \mu E \le 0$.

Also see

• Results about negative sets can be found here.

Sources

• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $4.1$