Uniformly Distributed Measures have Big Pieces of Lipschitz Graphs\n locally

2016/03/10 by A. Dali Nimer, Nimer, A. Dali
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1603.03415

openalex publication_date 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The study of uniformly distributed measures was crucial in Preiss' proof of\nhis theorem on rectifiability of measures with positive density. It is known\nthat the support of a uniformly distributed measure is an analytic variety. In\nthis paper, we provide quantitative information on the rectifiability of this\nvariety. Tolsa had already shown that n-uniform measures have Big Pieces of\nLipschitz Graphs(BPLG) . Here, we prove that a uniformly distributed measure\nhas BPLG locally.\n

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