# pr.chance – Modulus of continuity of parameterizing Wasserstein Answer

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## pr.chance – Modulus of continuity of parameterizing Wasserstein

Let $$x_1,dots,x_nin X$$ some urbanity house $$X$$ and let $$Delta$$ breathe the chance simplex in $$mathbb{R}^n$$. Consider the map sending some $$(w_1,dots,w_n)$$ to the finitely supported touchstone $$sum_{ok=1}^n w_kdelta_{x_n}$$. This map is clearly steady with respect to the Wasserstein distance, however is it too Lipschitz?

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