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In the paper we prove that, for $\kappa\in(0,8)$, the $n$-point boundaryGreen's function of exponent $\frac8\kappa -1$ for chordal SLE$_\kappa$ exists.We also prove that the convergence is uniform over compact sets and the Green'sfunction is continuous. We also give up-to-constant bounds for the Green'sfunction.

Existence of multi-point boundary Green's function for chordal Schramm-Loewner evolution (SLE)