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We define a quantitative stratification, which groups together points in the domain into quantitative weakly singular strata S^j_{\\eta,r}(u) according to the number of approximate symmetries of u at certain scales, and prove that their tubular neighborhoods have small volume, namely Vol(T_r(\\cS^j_{\\eta,r}(u))< Cr^{m+2-j-\\eps}. 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