Can you help me with the following question?
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with the property that $\int_{-\infty} ^\infty |f(t)|\,dt < +\infty$.
Show that for almost all $x\in \mathbb{R}$ (with respect to Lebesgue measure) the series $\sum_{n=1}^\infty f(nx+n!)$ converges and the formula $g(x):=\sum_{n=1}^\infty f(nx+n!)$ defines a Lebesgue integrable function on $\mathbb{R}$.