关于Eriksson-Bique和Soultanis在度量度量空间上建立的图表的注释

Pub Date : 2022-10-13 DOI:10.4153/s0008439523000486

Luca Gennaioli, N. Gigli

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引用次数: 0

摘要

本文的动机是Eriksson Bique和Soultanis最近关于在一般度量测度空间中构造图表的研究。我们分析了它们的构造，并提供了一个替代的、更简单的证明，证明这些图存在于有限Hausdorff维数的集合上。这里所做的观察也为研究$\text{RCD}$空间设置中参考测度和图表之间的关系提供了一些简化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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