The uniform boundary measure of the Brownian disk and half-plane is almost surely a constant multiple of the Hausdorff measure with gauge function h(s)=s^2 log log(1/s).
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The Hausdorff measure of the boundary of the Brownian disk
The uniform boundary measure of the Brownian disk and half-plane is almost surely a constant multiple of the Hausdorff measure with gauge function h(s)=s^2 log log(1/s).