Let $f$ be a measurable function from an Euclidean space to the reals. Is it true that the inverse image of every set of measure zero is also measurable?
2026-04-26 09:31:54.1777195914
Inverse image of sets of Lebesgue measure zero.
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It is not! See Remark 1.3.10 in Terrence Tao's Intro to Measure Theory--found here https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf