Let $T \in \text{Exp}(\theta)$ be an D214: Exponential random positive real number such that

(i)	$\mu_T$ is a D204: Probability distribution measure for $T$

Let $\ell$ be the D5645: Real Lebesgue measure.
Let $t \in \mathbb{R}$ be a D993: Real number.

Then \begin{equation} \frac{d \mu_T}{d \ell} (t) = \theta e^{- \theta t} I_{[0, \infty)} (t) \end{equation}