If non negative functions $f,g : \mathbb{R^n} \to [0, \infty]$ are measurable, then $f+g$ is measurable.

Question

Let $f, g : \mathbb{R^n} \to [0, \infty]$ are measurable. Then, prove that $f+g$ is measurable.

I know that if the value of $f,g$ is finite, $f+g$ is also measurable, but I cannot prove when the value of $f,g$ is in $[0, \infty]$ since I cannot know what I should do.

Please give me some ideas.