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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. "

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