Let $M = (\mathbb{R}^D, \mathcal{L}, \ell)$ be a D1744: Lebesgue measure space such that
| (i) | $\eta_0, \eta_1, \eta_2, \ldots : \mathbb{R}^D \to \mathbb{C}$ are each an D1921: Absolutely integrable function on $M$ |
| (ii) | \begin{equation} \lim_{n \to \infty} \int_{\mathbb{R}^D} \eta_n(x) \, \ell(d x) = a \end{equation} |
| (iii) | \begin{equation} \sup_{n \in \mathbb{N}} \int_{\mathbb{R}^D} |\eta_n(x)| \, \ell(d x) < \infty \end{equation} |
| (iv) | \begin{equation} \forall \, r > 0 : \lim_{n \to \infty} \int_{\mathbb{R}^D \setminus B(0, r)} |\eta_n(x)| \, \ell(d x) = 0 \end{equation} |
| (v) | $f : \mathbb{R}^D \to \mathbb{C}$ is a D5633: P-integrable complex Borel function on $M$ for $p \in [1, \infty)$ |
Then
\begin{equation}
\lim_{n \to \infty} \Vert \eta_n * f - a f \Vert_{L^p}
= 0
\end{equation}