Definition:Intersection Measure/Complex Measure

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

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

Let $F \in \Sigma$.

Then the intersection (complex) measure (of $\mu$ by $F$) is the mapping $\mu_F: \Sigma \to \C$, defined by:


 * $\map {\mu_F} E = \map \mu {E \cap F}$

for each $E \in \Sigma$.

Also see

 * Intersection Complex Measure is Complex Measure