I have a question regarding the example of a set that is Lebesgue measurable, but not a Borel set on $\mathbb{R}$ given in https://www.math3ma.com/blog/lebesgue-but-not-borel. Wouldn't it be the case that we have $N = f(f^{-1}(N)) = (f^{-1})^{-1}(f^{-1}(N))$ measurable following this analysis? We namely have that $f^{-1}$ is continuous, hence measurable and the inverse mappings of Lebesgue measurable sets under $f^{-1}$ are hence Lebesgue measurable..
2026-04-02 11:54:46.1775130886
Confusion about example of Lebesgue measurable set that is not Borel
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Umberto P. answered it in the comments: