Abstract The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13]. The proof, which is based on a quantitative differentiation argument, closely follows the original one. As a simple outcome we provide a volume estimate for the enlargement of Gigli-DePhilippis’ boundary ([20, Remark 3.8]) of ncRCD(K, N) spaces.

中文翻译：

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非塌陷 RCD 度量空间的定量奇异层的体积边界

摘要 本笔记的目的是将 Cheeger 和 Naber 在 [13] 中针对非塌陷 Ricci 极限获得的有效奇异层的体积边界推广到非塌陷 RCD(K, N) 度量空间的类别。该证明基于定量微分论证，与原始证明非常相似。作为一个简单的结果，我们为 ncRCD(K, N) 空间的 Gigli-DePhilippis 边界（[20，备注 3.8]）的扩大提供了体积估计。