A doubt. Exists a $f:X\to Y$ measurable function and $f^{-1}(B)$ is not measurable set for some $B\subset Y$?
2026-03-25 04:36:52.1774413412
measurable function and inverse image not measurable set.
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Take $f=\mathrm{Id}_X : X \to X$. Then for $B \subset X$ not mesurable, $f^{-1}(B)$ is not mesurable.