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}
}
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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  • Silvia Ghinassi
  • Mathematics
  • Annales Academiae Scientiarum Fennicae Mathematica
  • 2020
We say a measure is C d-rectifiable if there is a countable union of C d-surfaces whose complement has measure zero. We provide sufficient conditions for a Radon measure in R to be C d-rectifiable,Expand
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