TitleAn elementary rectifiability lemma and some applications
Publication TypeJournal Article
Year of Publication2023
AuthorsDe Lellis C, Fleschler I
Type of Articlegeometric measure theory
Abstract

We generalize a classical theorem of Besicovitch, showing that, for any positive integers k<n, if ERn is a Souslin set which is not Hk-σ-finite, then E contains a purely unrectifiable closed set F with 0<Hk(F)<. Therefore, if ERn is a Souslin set with the property that every closed subset with finite Hk measure is k-rectifiable, then E is k-rectifiable. We also point out that this theorem holds in a suitable class of metric spaces. Our interest is motivated by recent studies of the structure of the singular sets of several objects in geometric analysis and we explain the usefulness of our lemma with some examples.

Notes

Preprint

Order: 
12