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: <math>\begin{align}
& \Pr\big(X\in \overline{g^{-1}(F)}\big) \leq
\Pr\big(X\in g^{-1}(F)\cup D_g\big)
\le {} & \Pr\big(X \in g^{-1}(F)\big) + \Pr(X\in D_g) =
\Pr\big(g(X) \in F\big) + 0.
\end{align}</math>
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