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Four Function Theorems Through Optimal Transport and Entropic Analogs
We study entropic versions of four-function inequalities and give transport proofs of the Euclidean Ahlswede-Daykin theorem and a four-function version of the Prekopa-Leindler inequality due to Cordero-Erausquin and Maurey. One of our main results shows that the sharp range for the four-function ine
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