Corpus ID: 119144938

Quantitative Reifenberg theorem for measures

@article{Edelen2016QuantitativeRT,
  title={Quantitative Reifenberg theorem for measures},
  author={Nick Edelen and Aaron Naber and Daniele Valtorta},
  journal={arXiv: Classical Analysis and ODEs},
  year={2016}
}
We study generalizations of Reifenberg's Theorem for measures in $\mathbb R^n$ under assumptions on the Jones' $\beta$-numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which holds for general measures without density assumptions, give effective measure bounds on $\mu$ away from a closed $k$-rectifiable set with bounded Hausdorff measure. We show examples to see the sharpness of our results. Under further density assumptions one… Expand
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