Let $Z \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number such that
Let $\ell$ be the D5645: Real Lebesgue measure.
Let $t \in \mathbb{R}$ be a D993: Real number.
(i) | $\mu_Z$ is a D204: Probability distribution measure for $Z$ |
Let $t \in \mathbb{R}$ be a D993: Real number.
Then
\begin{equation}
\frac{d \mu_Z}{d \ell} (t)
=
\frac{1}{\sqrt{2 \pi}} e^{- t^2 / 2}
\end{equation}