## Abstract

We present an algebraic account of the Wasserstein distances

*W*on complete metric spaces, for_{p}*p*≥ 1. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in*p*, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric satisfies a property typical of the Wasserstein distance*W*. We show that the free complete such algebra over a complete metric space is that of the Radon probability measures with finite moments of order_{p}*p*, equipped with the Wasserstein distance as metric and with the usual binary convex sums as operations.Original language | English |
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Article number | 4826 |

Number of pages | 18 |

Journal | Logical Methods in Computer Science |

Volume | 14 |

Issue number | 3 |

DOIs | |

Publication status | Published - 14 Sep 2018 |