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 :


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