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math.MG2021
A natural compactification of the Gromov-Hausdorff space
Hiroki Nakajima, Takashi Shioya
In this paper, we introduce a pseudometric on the family of isometry classes of (extended) metric spaces. Using it, we obtain a natural compactification of the Gromov-Hausdorff spa…
math.MG2021
Convergence of group actions in metric measure geometry
Hiroki Nakajima, Takashi Shioya
We generalize the box and observable distances to those between metric measure spaces with group actions, and prove some fundamental properties. As an application, we obtain an exa…