Let $f \in C_{b}(\mathbb{R})$ and let $(\delta_{n})$ be a sequence of functions forming an approximate identity. Show that the sequence $\left(f * \delta_{n}\right)_{n \in \mathbb{N}}$ converges pointwise to $f$ on $\mathbb{R}$.
Let $f \in C_{b}(\mathbb{R})$ and let $(\delta_{n})$ be a sequence of functions forming an approximate identity.\\
Show that the sequence $\left(f * \delta_{n}\right)_{n \in \mathbb{N}}$ converges pointwise to $f$ on $\mathbb{R}$.