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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 topic always have the completeness hypothesis and it seems to be an important requirement for the associated Wasserstein metric to have nice properties. I'm wondering if it's possible to make sense of ${\sf CD}(K,N)$ condition, say, in the case of locally complete metric measure spaces. I'm aware of the existence of ${\sf CD}_{\text{loc}}(K,N)$ condition, but even in that case it's usual to assume completeness on the whole space. Thanks in advance for your comments.

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