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 $(1+\kappa/8)$-dimensional Minkowski content. 
Laurence S. Field
math.PR