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In Alfred Galichon's book Optimal Transport Methods in Economics the foollowing result is stated for OT problems on the real line. Theorem 4.3.(i) Assume that $\Phi$ is supermodular. Then the primal ...

$\DeclareMathOperator\marg{marg}$I would like to know if the following problem can be studied as an optimal transport problem, possibly imposing additional assumptions on the data. Consider two sets $\...

Question: Are there any good references for facts about function-valued random variables? In particular for facts like the following: Let $X$ be a topological space, $Y$ be a random variable with ...

The question about throwing darts asked on the MathOverflow page Sacred Geometry of Chance was not well received, apparently because of "[t]oo much noise around the actual math", as stated in a well-...

In Theorem 14.37 of Variational Analysis by Rockafellar and Wets, it shows that for any normal integrand $f:T\times\mathbb{R}^n\to\overline{\mathbb{R}}$, the function $p:T\to\overline{\mathbb{R}}$ ...