Characterization of rectifiable measures in terms of α-numbers

JONAS AZZAM, XAVIER TOLSA, TATIANA TORO

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We characterize Radon measures μ in Rn that are d-rectifiable in the sense that their supports are covered up to μ-measure zero by countably many d-dimensional Lipschitz images and μ≪Hd. The characterization is in terms of a Jones function involving the so-called α-numbers. This answers a question left open in a former work by Azzam, David, and Toro.
Original languageEnglish
Pages (from-to)7991-8037
Number of pages47
JournalTransactions of the American Mathematical Society
Volume373
Issue number11
DOIs
Publication statusPublished - 1 Jan 2020

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