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https://mathoverflow.net/questions/509834/measurability-of-the-geodesic-map-on-the-wasserstein-space
riemannian geometry - Measurability of the geodesic map on the Wasserstein space - MathOverflow
Let $M$ be a smooth closed Riemannian manifold and $\mathcal{P}$ the space of probability measures on $M$ endowed with the $W_2$-distance, namely: $$...
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