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 $\mathbb{R}^N$
(ii)	$f : \mathbb{R}^N \to \mathbb{C}$ is a D5633: P-integrable complex Borel function on $M$ for $p \in [1, \infty)$

Then \begin{equation} \lim_{\varepsilon \to \infty} \Vert \eta_\varepsilon * f - f \Vert_{L^p} = 0 \end{equation}