Measurable function
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In mathematics, a measurable function is a function <math>f</math> from a measure space <math>(X, \mu)</math> to the real numbers (possibly including <math>\pm \infty</math>) that satisfies that <math>f^{-1}((c, \infty])</math> is measurable in <math>X</math> for all <math>c \in [-\infty, \infty]</math>.