Consider the Wasserstein metric W_1 on the set of probability measures on a compact metric space. I wonder how many balls of radius $\epsilon$ for $\epsilon\in \mathbb R^+$ is needed to cover a ball of size 2 $\epsilon$? Are there known estimates (lower or upper bound) depending on $\epsilon$ for this number?
2026-02-24 10:14:27.1771928067
ball in the Wasserstein space W_1
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