= Harmonic capacity from infinity in the upper half-plane
{title2=$\operatorname{cap}(K)=\lim_{y\to\infty}\pi y\,\mathbb P_{iy}(B_{T(\mathbb H\setminus K)}\in K)$}
This capacity measures the asymptotic probability that <planar Brownian motion> hits a <compact H-hull> before the real axis. It scales linearly with length and is distinct from <half-plane capacity>. A vertical slit of height $h$ has capacity $2h$; a half-disc of radius $r$ has capacity $4r$. Monotonicity of Brownian hitting probabilities gives $\operatorname{cap}(K)\le4\operatorname{rad}(K)$, where the radius is that of the least real-centred enclosing half-disc. For finite slit hulls the capacity is the length of the image of the two-sided absorbing boundary under the <mapping-out function>.
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