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We consider a transient chordal SLE$_\kappa(\rho_1,\dots,\rho_m)$ curve$\eta$ in $\mathbb{H}$ from $w$ to $\infty$ with force points $ v_1> \cdots>v_m$ in $(-\infty,w^-]$, which intersects and is not boundary-filling on$(-\infty,v_m)$. The main result is that there is an atomless locally finiteBorel measure $\mu_\eta$ on $\eta\cap (-\infty,v_m]$ such that for any $v<v_m$,the $d$-dimensional Minkowski content of $\eta\cap [v,v_m]$ exists and equals$\mu_\eta [v,v_m]$, where $d=\frac{(\sum \rho_j+4)(\kappa-4-2\sum\rho_j)}{2\kappa}$ is the Hausdorff dimension of $\eta\cap [v,v_m]$. In thecase that all $\rho_j=0$, this measure agrees with the covariant measurederived in [Alberts-Sheffield, 2011] for chordal SLE$_\kappa$ up to amultiplicative constant. %Such measure, called Minkowski content measure,satisfies conformal covariance properties. We call such measure a Minkowskicontent measure, extend it to a class of subsets of ${\mathbb{R}}^n$, and provethat they satisfy conformal covariance. To construct the Minkowski contentmeasure on $\eta\cap [v,v_m]$, we follow the standard approach to derive theexistence and estimates of the one- and two-point boundary Green's functions of$\eta$ on $(-\infty,v_m)$, which are the limits of the rescaled probabilitythat $\eta$ passes through small discs or open real intervals centered atpoints on $(-\infty,v_m)$.

Boundary Green's functions and Minkowski content measure of multi-force-point SLE$_\kappa(\underline\rho)$