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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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Expected value of the quotient times quotient of the expected values
I am looking for a reference -if there is any- about how to control the following expression:
$$\mathbb{E}\left[\frac{f(X)}{g(X)}\right]\cdot\frac{\mathbb{E}[g(X)]}{\mathbb{E}[f(X)]},$$
where $f$ and …