Exact Hausdorff gauges for SLE

Resolves Schramm’s Hausdorff-measure question for chordal SLE_κ, $0\lt \kappa\lt 8$. The explicit gauge $r^d(\log\log(1/r))^{(2-d)/2}$, $d=1+\kappa/8$, gives almost surely positive finite measure to every trace segment $\gamma([s,t])$ with $0\lt s\lt t\lt \infty$, and finite expected measure to the trace in every bounded disk.