  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.
