Let $M = (\mathbb{R}^N, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space such that
(i) | $\eta = \{ \eta_{\varepsilon} \}_{\varepsilon \in (0, \infty)}$ is a D138: Standard mollifier for $\mathbb{R}^N$ |
Then
\begin{equation}
\forall \, \varepsilon > 0 :
\int_{\mathbb{R}^N} \eta_{\varepsilon}(x) \, \ell(d x)
= 1
\end{equation}