One can show that there are non-Borel measurable sets (A subset mathbb{R}), see Appendix (mathrm{G}). Taking this

Question:

One can show that there are non-Borel measurable sets $A \subset \mathbb{R}$, see Appendix $\mathrm{G}$. Taking this fact for granted, show that measurability of $|u|$ does not, in general, imply measurability of $u$. (The converse is, of course, true: measurability of $u$ always guarantees that of $|u|$.)

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