ThmDex – An index of mathematical definitions, results, and conjectures.
F10708
Formulation 0
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}