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arXiv 2210.07010math.MG
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关于度量测度空间上Eriksson-Bique和Soultanis图的注记

A note about charts built by Eriksson-Bique and Soultanis on metric measure spaces

Luca Gennaioli, Nicola Gigli

摘要:

这一说明的动机是最近的研究Eriksson Bique和Soultanis关于建设图在一般度量测度空间。我们分析他们的建设,并提供了一个替代和更简单的事实证明,这些图表存在于有限的豪斯多夫维数。本文的观察也为研究$\text{RCD}$空间中的参考测度与图之间的关系提供了一些简化。

英文摘要:

This note is motivated by recent studies by Eriksson-Bique and Soultanis about the construction of charts in general metric measure spaces. We analyze their construction and provide an alternative and simpler proof of the fact that these charts exist on sets of finite Hausdorff dimension. The observation made here offers also some simplification about the study of the relation between the reference measure and the charts in the setting of $\text{RCD}$ spaces.

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