# Effective Reifenberg theorems in Hilbert and Banach spaces

@article{Edelen2018EffectiveRT,
title={Effective Reifenberg theorems in Hilbert and Banach spaces},
author={Nick Edelen and Aaron Naber and Daniele Valtorta},
journal={Mathematische Annalen},
year={2018},
pages={1-80}
}
• Published 4 June 2018
• Mathematics
• Mathematische Annalen
A famous theorem by Reifenberg states that closed subsets of $$\mathbb {R}^n$$Rn that look sufficiently close to k-dimensional at all scales are actually $$C^{0,\gamma }$$C0,γ equivalent to k-dimensional subspaces. Since then a variety of generalizations have entered the literature. For a general measure $$\mu$$μ in $$\mathbb {R}^n$$Rn, one may introduce the k-dimensional Jones’ $$\beta$$β-numbers of the measure, where $$\beta ^k_\mu (x,r)$$βμk(x,r) quantifies on a given ball $$B_r(x)$$Br(x… Expand
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