# What is the “nicest” type of function guaranteed to exist in every equivalence class of $L^p(\mathbb{R})$, for $1\leq p < \infty?$

For example, given assumptions on the weak derivatives, one can sometimes conclude that an equivalence class in $$W^{k,p}$$ has a continuous modification. It's false that every equivalence class in $$L^p$$ has a continuous modification, but what is the "best" adjective that one can replace "continuous" with?

In other words, would you care to complete the following sentence?

"Every equivalence class in $$L^p(\mathbb{R})$$ has a _________ representative. "