Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of metric measure spaces satisfying the CD condition for
  negative values of the dimension parameter   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.

5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg