Suppose $f$ is a real-valued function on $\mathbb R$ such that $f^{−1}(c)$ is measurable for each number $c$. Is $f$ necessarily measurable?
Must $f$ be measurable if each $f^{-1}(c)$ is?
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real-analysis
measure-theory
lebesgue-integral
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0What does the notation 1(c) mean? – 2012-12-24