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Getting Wasserstein closeness from a derivative estimate

In my setting, $\mu$ and $\nu$ are probability measures on $\mathbb{R}^{2}$ with compact support. For any function $f\in{C^{2}_{b}(\mathbb{R}^{2})}$, I have the estimate: $$ |\mathbb{E}_{\mu}(f)-\math …
David Pechersky's user avatar