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Let $(M,g_0)$ be a compact Riemannian manifold and $\\mathcal{C}(M,g_0)$ the class of manifolds $(M,g)$ conformal to $(M,g_0)$. In this paper we use $\\varepsilon$-regularity to show a rigidity result in the conformal class $\\mathcal{C}(S^n,g_0)$ of standard sphere under $L^p$-scalar rigidity condition. 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