Definition:Intersection Measure

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

Let $F \in \Sigma$.

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


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

for each $E \in \Sigma$.

Also see

 * Intersection Measure is Measure shows that $\mu_F$ is indeed a measure on $\struct {X, \Sigma}$.