Two-sided radial SLE and length-biased chordal SLE

We show that, for $\kappa \le 4$, the integral of the two-sided radial SLE${}_{\kappa }$ measures over all interior points is chordal SLE${}_{\kappa }$ biased by the path’s natural length, which is its $(1+\kappa \mathrm{/}8)$-dimensional Minkowski content.