Integral with respect to Dirac Measure

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

Let $x \in X$, and let $\delta_x$ be the Dirac measure at $x$.

Let $f \in \MM _{\overline \R}, f: X \to \overline \R$ be a measurable function.

Then:


 * $\ds \int f \rd \delta_x = \map f x$

where the integral sign denotes the $\delta_x$-integral.