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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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(Sharp) Bounds on $E(XYZ)$ given all the bivariate marginals
Suppose $X,Y,Z$ are all real-valued random variables. Suppose I know the joint marginal distributions of $(X,Y)$, $(Y,Z)$ and $(X,Z)$. I want to find bounds on $E(XYZ)$.
In the case of bounding $E(XY) …