满足维数参数为负值的CD条件的度量测度空间的收敛性
Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter
摘要：
研究了在适当的收敛性概念下，广义维数参数为负值的曲率维数条件是否稳定的问题。为此，首先，我们引入一个适当的设置，以引入CD（K，N）-条件$N < 0$，允许度规测量结构中的参考措施是准氡。然后在这类空间中，我们引入$d_{\mathsf{iKRW}}$，它扩展了度量测度空间之间的距离的现有概念。最后，证明了如果满足CD（K，N）-条件的度量测度空间序列关于$N < 0$到某个度量测度空间的距离收敛，则该极限结构仍是CD（K，N）空间.
英文摘要：
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.
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