*Submitted Paper*

**Inserted:** 7 apr 2021

**Last Updated:** 7 apr 2021

**Year:** 2021

**Abstract:**

We study the problem of whether the curvature-dimension condition with negative values of the generalized dimension parameter is stable under a suitable notion of convergence. To this purpose, first of all we introduce an appropriate setting to introduce the CD(K, N)-condition for $N < 0$, allowing metric measure structures in which the reference measure is quasi-Radon. Then in this class of spaces we introduce the distance $d_{\mathsf{iKRW}}$, which extends the already existing notions of distance between metric measure spaces. Finally, we prove that if a sequence of metric measure spaces satisfying the CD(K, N)-condition with $N < 0$ is converging with respect to the distance $d_{\mathsf{iKRW}}$ to some metric measure space, then this limit structure is still a CD(K, N) space.

**Download:**