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Such limits $Y$ may be quite singular, however it is known that there is a subset of full measure $\\cR(Y)\\subseteq Y$, called {\\it regular} points, along with coverings by the almost regular points $\\cap_\\epsilon \\cup_r\\cR_{\\epsilon,r}(Y)=\\cR(Y)$ such that each of the {\\it Reifenberg sets} $\\cR_{\\epsilon,r}(Y)$ is bi-H\\\"older homeomorphic to a manifold. 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