Definition:Intersection Measure

Definition
Let $\left({X, \mathcal A, \mu}\right)$ be a measure space.

Let $F \in \mathcal A$.

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


 * $\mu_F \left({A}\right) = \mu \left({A \cap F}\right)$

It is in fact a measure on $\left({X, \mathcal A}\right)$, as shown on Intersection Measure is Measure.