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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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Convexity of a set of probability densities

Consider the space of probability densities $(P(\mathbb{R}^d), W_2)$ (probability measures on $\mathbb{R}^d$ with 2-Wasserstein distance). How can we determine if a subset $Q$ is convex? I know that a …