*Published Paper*

**Inserted:** 19 jun 2004

**Last Updated:** 23 sep 2015

**Journal:** J. Eur. Math. Soc.

**Volume:** 8

**Number:** 3

**Pages:** 415-434

**Year:** 2006

**Doi:** 10.4171/JEMS/61

**Abstract:**

Given a metric space $X$ we consider a general class of functionals which measure the cost of a path in $X$ joining two given points $x_0$ and $x_1$, providing abstract existence results for optimal paths. The results are then applied to the case when $X$ is a Wasserstein space of probabilities on a given set $\Omega$ and the cost of a path depends on the value of classical functionals over measures. Conditions to link arbitrary extremal measures $\mu_1$ and $\mu_2$ by means of finite cost paths are given.

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