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user 48839
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Using the Stone-Weierstrass theorem to solve an integral limit
Since $f$ is increasing, $\mu(0,x)=f(x)$ defines a (here: continuous) measure on $[0,c]$, which we can also view as a measure on $\mathbb R$ with support in this set. By Fubini, the RHS equals
$$
\fra …
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