I'm studying for a qualifying exam and having difficulty showing the following:
Let $f\in L^1_{loc}(\mathbb{R})$ be a real-valued locally integrable function. Suppose that for each positive integer, $f(x+1/n)\geq f(x)$ for almost every $x\in \mathbb{R}$. Show that for each real number $a\geq 0$, $f(x+a)\geq f(x)$ for almost every $x\in\mathbb{R}$.
How to approach this type of problem?