Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces

<jats:title>Abstract</jats:title>
<jats:p>The aim of this note is to generalize to the class of non collapsed RCD(<jats:italic>K</jats:italic>, <jats:italic>N</jats:italic>) 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(<jats:italic>K</jats:italic>, <jats:italic>N</jats:italic>) spaces.</jats:p>