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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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Wasserstein interpolation between two probability measures on a metric space

The following discussion is based on the book Gradient Flows by Ambrosio, Gigli, and Savare (2008). Consider $p$-Wasserstein distance with $p>1$ on a Hilbert space (for the sake of uniqueness). Let $ …
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