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Consider a point $x\\in \\partial B_1$ and let $n(x)$ denote the unit normal vector at $x$. Let $\\alpha$ be a number in $(-1,n-1]$ and $A \\in [0,+\\infty) $. We prove that $u(x+n(x)t)t^{\\alpha} \\to A$ as $t \\to +0$ if and only if $\\frac{\\mu({B_r(x)})}{r^{n-1}} r^{\\alpha} \\to C_\\alpha A$ as $r\\to+0$, where ${C_\\alpha= \\frac{\\pi^{n/2}}{\\Gamma(\\frac{n-\\alpha+1}{2})\\Gamma(\\frac{\\alpha+1}{2})}}$. 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