Characterization of rectifiable measures in terms of α-numbers

JONAS AZZAM; XAVIER TOLSA; TATIANA TORO

doi:10.1090/TRAN/8170

Characterization of rectifiable measures in terms of α-numbers

JONAS AZZAM, XAVIER TOLSA, TATIANA TORO

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	7991-8037
Number of pages	47
Journal	Transactions of the American Mathematical Society
Volume	373
Issue number	11
DOIs	https://doi.org/10.1090/TRAN/8170
Publication status	Published - 1 Jan 2020

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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.",

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Characterization of rectifiable measures in terms of α-numbers

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