If $|f|$ is (lebesgue) measurable, does that imply that $f$ measurable? My intuition tells me that it doesn't but I don't know how to show that. Thanks
2026-04-11 16:51:21.1775926281
If |f| is (lebesgue) measurable, is f measurable?
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Hint: a function $f$ taking on only values $\pm 1$ can behave very rudely, but we would have $|f| = 1$.