\begin{definition}[Definition:Intersection Measure]
Let $\left({X, \Sigma, \mu}\right)$ 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:
:$\mu_F \left({E}\right) = \mu \left({E \cap F}\right)$
It is in fact a measure on $\left({X, \Sigma}\right)$, as shown on Intersection Measure is Measure.
{{expand|verify name, Schilling gives none}}
\end{definition}