Definition 16.1.3 (Positive/Negative/Null Sets). Let $(X, \cm)$ be a measurable space, $\mu: \cm \to [-\infty, \infty]$ be a signed measure, and $A \in \cm$, then $A$ is...

1. positive if $\mu(B) \ge 0$ for all $B \in \cm$ with $B \subset A$.

2. negative if $\mu(B) \le 0$ for all $B \in \cm$ with $B \subset A$.

3. null if $\mu(B) = 0$ for all $B \in \cm$ with $B \subset A$.