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arXiv · 2304.06878

Topological aspects of the space of metric measure spaces

Daisuke Kazukawa·Hiroki Nakajima·Takashi Shioya
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Abstract

Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several topological properties on the space equipped with these distance functions toward a deep understanding of convergence theory.

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Daisuke Kazukawa, Hiroki Nakajima, Takashi Shioya. 2023-04-14. Topological aspects of the space of metric measure spaces. https://arxiv.org/abs/2304.06878

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