# Definition:Intersection Measure

## Definition

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.

## Sources

- 2005: René L. Schilling:
*Measures, Integrals and Martingales*... (previous) ... (next): $\S 4$: Problem $7$