摘要：We present an algebraic account of the Wasserstein distances $W_p$ oncomplete metric spaces, for $p \geq 1$. This is part of a program of aquantitative algebraic theory of effects in programming languages. Inparticular, we give axioms, parametric in $p$, for algebras over metric spacesequipped with probabilistic choice operations. The axioms say that theoperations form a barycentric algebra and that the metric satisfies a propertytypical of the Wasserstein distance $W_p$. We show that the free complete suchalgebra over a complete metric space is that of the Radon probability measureswith finite moments of order $p$, equipped with the Wasserstein distance asmetric and with the usual binary convex sums as operations.
