Assume that $f \in L^{1}(\mathbb{R})$ and $g \in C_{b}(\mathbb{R})$. a) Show that $f * g$ is continuous. b) Show that if $g$ is uniformly continuous on $\mathbb{R}$, then $f * g$ is uniformly continuous on $\mathbb{R}$.
Assume that $f \in L^{1}(\mathbb{R})$ and $g \in C_{b}(\mathbb{R})$.\\
a) Show that $f * g$ is continuous.\\
b) Show that if $g$ is uniformly continuous on $\mathbb{R}$, then $f * g$ is uniformly continuous on $\mathbb{R}$.