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arXiv · 1603.03415

Uniformly Distributed Measures have Big Pieces of Lipschitz Graphs locally

A. Dali Nimer
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Abstract

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

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A. Dali Nimer. 2016-03-10. Uniformly Distributed Measures have Big Pieces of Lipschitz Graphs locally. https://arxiv.org/abs/1603.03415

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