Show that $C^{0}(\mathbf{R}) \cap CL(\mathbf{R}) \subset L^{1}(\varphi)$. We admit throughout the rest of the problem that $\int_{-\infty}^{+\infty} \varphi(t) \mathrm{d}t = 1$.
Show that $C^{0}(\mathbf{R}) \cap CL(\mathbf{R}) \subset L^{1}(\varphi)$.
We admit throughout the rest of the problem that $\int_{-\infty}^{+\infty} \varphi(t) \mathrm{d}t = 1$.