{"paper":{"title":"Effective Reifenberg theorems in Hilbert and Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Aaron Naber, Daniele Valtorta, Nicholas Edelen","submitted_at":"2018-06-04T17:41:21Z","abstract_excerpt":"The aim of this article is to study effective Reifenberg theorems for measures in a Hilbert or Banach space. For Hilbert spaces, we see all the results from $\\mathbb{R}^n$ continue to hold with no additional restrictions. For a general Banach spaces we will see that the classical Reifenberg theorem holds, and that a weak version of the effective Reifenberg theorem holds in that if one assumes a summability estimate $\\int_0^2 \\beta^k(x,r)^1 \\frac{dr}{r}