It is known that if $g_n: \mathbb{R} \rightarrow \mathbb{R}$, $n=1,2,...$, is in $C_c^{\infty}(\mathbb{R})$, $ \int_\mathbb{R} g_n(x)dx=1$, $supp(g_n) \subset (-r_n,r_n)$,where $0
Let now $$g_n(x)=\frac{1}{\pi} \frac{r_n}{r_n^2+x^2},$$ $x\in \mathbb{R}$, $n \in \mathbb{N}$, where $0 Is it also true that if $f$ integrable and continuous, then $f*g_n(x) \rightrightarrows f(x)$ on compact subsets of $\mathbb{R}$? Thanks in advance!