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Under the assumption that a normal curvature term is small, namely if for the normal map $u$ we have for some $s \\in (\\frac{1}{2},1)$\n  $$ \\int_{B} \\int_{B} \\left | \\frac{u_k(x) \\wedge u_k(y)}{|x-y|^{s}} \\right|^{\\frac{2}{s}}\\, \\frac{dx\\, dy}{|x-y|^{2}} < \\varepsilon $$ then we show that we can either pass to the limit and obtain an almost everywhere immersion $\\Phi$ or $\\Phi$ collapses and is constant. 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