# Approximating a bounded measurable function from below by a sequence of smooth functions

Suppose that $$f: \mathbb{R} \to \mathbb{R}$$ is a bounded measurable function.

Is it possible to find a sequence of functions $$\{f_n \}_n: \mathbb{R} \to \mathbb{R}$$ in $$C^{\infty}_c( \mathbb{R})$$ such that $$f_n(x) \uparrow f(x)$$, for every $$x \in \mathbb{R}$$?

This seems to be true without the assumption that the convergence is from below, by standard results from the literature. However, I am really not sure about this case.