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Suppose that we have a parametric distribution $P_{\theta}$, which is indexed by the parameter $\theta \in \mathbb{R}^d$. Let $W\{\cdot,\cdot\}$ be the Wasserstein Metric between two distributions. ...

Let $\mu$ be a compactly supported absolutely continuous probability measure. Let $v,u$ be Lipschitz vector fields. For a vector field $w$ recall that $\Phi_t^w$ denotes its flow. A classical estimate ...

That's basically it. I would like to know if it's possible to define the ${\sf CD}(K,N)$ condition for metric measure spaces that are not necessarily complete. The references I have found on this ...