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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

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Upper bound of Wasserstein distance given by subvariables of codim 1

recently I am considering the upper-bound of Wasserstain distance. Say we have random vectors $X,Y$ of dimension $n$, and let $\tilde{X}_i (\tilde{Y}_i,$ resp.) be the $(n-1)$-dim random vector of $X …